Solve -8(5 - a) 2(-3a - 3)-8(-8 a)

Question

Simplify the expression

256 a + 240 - 48 a^{2}

Evaluate

- 8 (5 - a) \times 2 (- 3 a - 3) - 8 (- 8 a)

Multiply the terms

- 16 (5 - a) (- 3 a - 3) - 8 (- 8 a)

Multiply the numbers

More Steps

Evaluate

8 (- 8)

Multiplying or dividing an odd number of negative terms equals a negative

- 8 \times 8

Multiply the numbers

- 64

- 16 (5 - a) (- 3 a - 3) - (- 64 a)

Rewrite the expression

- 16 (5 - a) (- 3 a - 3) + 64 a

Expand the expression

More Steps

Calculate

- 16 (5 - a) (- 3 a - 3)

Simplify

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Evaluate

- 16 (5 - a)

Apply the distributive property

- 16 \times 5 - (- 16 a)

Multiply the numbers

- 80 - (- 16 a)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

- 80 + 16 a

(- 80 + 16 a) (- 3 a - 3)

Apply the distributive property

- 80 (- 3 a) - (- 80 \times 3) + 16 a (- 3 a) - 16 a \times 3

Multiply the numbers

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Evaluate

- 80 (- 3)

Multiplying or dividing an even number of negative terms equals a positive

80 \times 3

Multiply the numbers

240

240 a - (- 80 \times 3) + 16 a (- 3 a) - 16 a \times 3

Multiply the numbers

240 a - (- 240) + 16 a (- 3 a) - 16 a \times 3

Multiply the terms

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Evaluate

16 a (- 3 a)

Multiply the numbers

- 48 a \times a

Multiply the terms

- 48 a^{2}

240 a - (- 240) - 48 a^{2} - 16 a \times 3

Multiply the numbers

240 a - (- 240) - 48 a^{2} - 48 a

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

240 a + 240 - 48 a^{2} - 48 a

Subtract the terms

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Evaluate

240 a - 48 a

Collect like terms by calculating the sum or difference of their coefficients

(240 - 48) a

Subtract the numbers

192 a

192 a + 240 - 48 a^{2}

192 a + 240 - 48 a^{2} + 64 a

Solution

More Steps

Evaluate

192 a + 64 a

Collect like terms by calculating the sum or difference of their coefficients

(192 + 64) a

Add the numbers

256 a

256 a + 240 - 48 a^{2}

Show Solution

Factor the expression

16 (16 a + 15 - 3 a^{2})

Evaluate

- 8 (5 - a) \times 2 (- 3 a - 3) - 8 (- 8 a)

Multiply the terms

- 16 (5 - a) (- 3 a - 3) - 8 (- 8 a)

Multiply the numbers

More Steps

Evaluate

8 (- 8)

Multiplying or dividing an odd number of negative terms equals a negative

- 8 \times 8

Multiply the numbers

- 64

Evaluate

- 64 a

- 16 (5 - a) (- 3 a - 3) - (- 64 a)

Rewrite the expression

- 16 (5 - a) (- 3 a - 3) + 64 a

Simplify

More Steps

Evaluate

- 16 (5 - a) (- 3 a - 3)

Simplify

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Evaluate

- 16 (5 - a)

Apply the distributive property

- 16 \times 5 - 16 (- a)

Multiply the terms

- 80 - 16 (- a)

Multiply the terms

- 80 + 16 a

(- 80 + 16 a) (- 3 a - 3)

Apply the distributive property

- 80 (- 3 a) - 80 (- 3) + 16 a (- 3 a) + 16 a (- 3)

Multiply the terms

More Steps

Evaluate

- 80 (- 3)

Multiplying or dividing an even number of negative terms equals a positive

80 \times 3

Multiply the numbers

240

240 a - 80 (- 3) + 16 a (- 3 a) + 16 a (- 3)

Multiply the terms

More Steps

Evaluate

- 80 (- 3)

Multiplying or dividing an even number of negative terms equals a positive

80 \times 3

Multiply the numbers

240

240 a + 240 + 16 a (- 3 a) + 16 a (- 3)

Multiply the terms

More Steps

Evaluate

16 a (- 3 a)

Multiply the numbers

- 48 a \times a

Multiply the terms

- 48 a^{2}

240 a + 240 - 48 a^{2} + 16 a (- 3)

Multiply the terms

More Steps

Evaluate

16 (- 3)

Multiplying or dividing an odd number of negative terms equals a negative

- 16 \times 3

Multiply the numbers

- 48

240 a + 240 - 48 a^{2} - 48 a

240 a + 240 - 48 a^{2} - 48 a + 64 a

Calculate the sum or difference

More Steps

Evaluate

240 a - 48 a + 64 a

Collect like terms by calculating the sum or difference of their coefficients

(240 - 48 + 64) a

Calculate the sum or difference

256 a

256 a + 240 - 48 a^{2}

Solution

16 (16 a + 15 - 3 a^{2})

Show Solution

Find the roots

a_{1} = \frac{8 - 109}{3}, a_{2} = \frac{8 + 109}{3}

Alternative Form

a_{1} \approx - 0.813436, a_{2} \approx 6.146769

Evaluate

- 8 (5 - a) \times 2 (- 3 a - 3) - 8 (- 8 a)

To find the roots of the expression,set the expression equal to 0

- 8 (5 - a) \times 2 (- 3 a - 3) - 8 (- 8 a) = 0

Multiply the terms

- 16 (5 - a) (- 3 a - 3) - 8 (- 8 a) = 0

Multiply the numbers

More Steps

Evaluate

8 (- 8)

Multiplying or dividing an odd number of negative terms equals a negative

- 8 \times 8

Multiply the numbers

- 64

- 16 (5 - a) (- 3 a - 3) - (- 64 a) = 0

Rewrite the expression

- 16 (5 - a) (- 3 a - 3) + 64 a = 0

Calculate

More Steps

Evaluate

- 16 (5 - a) (- 3 a - 3) + 64 a

Expand the expression

More Steps

Calculate

- 16 (5 - a) (- 3 a - 3)

Simplify

(- 80 + 16 a) (- 3 a - 3)

Apply the distributive property

- 80 (- 3 a) - (- 80 \times 3) + 16 a (- 3 a) - 16 a \times 3

Multiply the numbers

240 a - (- 80 \times 3) + 16 a (- 3 a) - 16 a \times 3

Multiply the numbers

240 a - (- 240) + 16 a (- 3 a) - 16 a \times 3

Multiply the terms

240 a - (- 240) - 48 a^{2} - 16 a \times 3

Multiply the numbers

240 a - (- 240) - 48 a^{2} - 48 a

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

240 a + 240 - 48 a^{2} - 48 a

Subtract the terms

192 a + 240 - 48 a^{2}

192 a + 240 - 48 a^{2} + 64 a

Add the terms

More Steps

Evaluate

192 a + 64 a

Collect like terms by calculating the sum or difference of their coefficients

(192 + 64) a

Add the numbers

256 a

256 a + 240 - 48 a^{2}

256 a + 240 - 48 a^{2} = 0

Rewrite in standard form

- 48 a^{2} + 256 a + 240 = 0

Multiply both sides

48 a^{2} - 256 a - 240 = 0

Substitute a= 48,b= - 256 and c= - 240 into the quadratic formula a = \frac{- b \pm b ^{2} - 4 a c}{2 a}

a = \frac{256 \pm ( - 256 ) ^{2} - 4 \times 48 ( - 240 )}{2 \times 48}

Simplify the expression

a = \frac{256 \pm ( - 256 ) ^{2} - 4 \times 48 ( - 240 )}{96}

Simplify the expression

More Steps

Evaluate

(- 256)^{2} - 4 \times 48 (- 240)

Multiply

More Steps

Multiply the terms

4 \times 48 (- 240)

Rewrite the expression

- 4 \times 48 \times 240

Multiply the terms

- 46080

(- 256)^{2} - (- 46080)

Rewrite the expression

25 6^{2} - (- 46080)

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

25 6^{2} + 46080

Rewrite the expression

65536 + 46080

Add the numbers

111616

a = \frac{256 \pm 111616}{96}

Simplify the radical expression

More Steps

Evaluate

111616

Write the expression as a product where the root of one of the factors can be evaluated

1024 \times 109

Write the number in exponential form with the base of 32

3 2^{2} \times 109

The root of a product is equal to the product of the roots of each factor

3 2^{2} \times 109

Reduce the index of the radical and exponent with 2

32109

a = \frac{256 \pm 32 109}{96}

Separate the equation into 2 possible cases

a = \frac{256 + 32 109}{96} a = \frac{256 - 32 109}{96}

Simplify the expression

More Steps

Evaluate

a = \frac{256 + 32 109}{96}

Divide the terms

More Steps

Evaluate

\frac{256 + 32 109}{96}

Rewrite the expression

\frac{32 ( 8 + 109 )}{96}

Cancel out the common factor 32

\frac{8 + 109}{3}

a = \frac{8 + 109}{3}

a = \frac{8 + 109}{3} a = \frac{256 - 32 109}{96}

Simplify the expression

More Steps

Evaluate

a = \frac{256 - 32 109}{96}

Divide the terms

More Steps

Evaluate

\frac{256 - 32 109}{96}

Rewrite the expression

\frac{32 ( 8 - 109 )}{96}

Cancel out the common factor 32

\frac{8 - 109}{3}

a = \frac{8 - 109}{3}

a = \frac{8 + 109}{3} a = \frac{8 - 109}{3}

Solution

a_{1} = \frac{8 - 109}{3}, a_{2} = \frac{8 + 109}{3}

Alternative Form

a_{1} \approx - 0.813436, a_{2} \approx 6.146769

Show Solution