Solve 4x(x^2 - 3) - 2(x - 5)

Question

Simplify the expression

Solution

4 x^{3} - 14 x + 10

Evaluate

4 x (x^{2} - 3) - 2 (x - 5)

Expand the expression

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Calculate

4 x (x^{2} - 3)

Apply the distributive property

4 x \times x^{2} - 4 x \times 3

Multiply the terms

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Evaluate

x \times x^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{1 + 2}

Add the numbers

x^{3}

4 x^{3} - 4 x \times 3

Multiply the numbers

4 x^{3} - 12 x

4 x^{3} - 12 x - 2 (x - 5)

Expand the expression

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Calculate

- 2 (x - 5)

Apply the distributive property

- 2 x - (- 2 \times 5)

Multiply the numbers

- 2 x - (- 10)

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

- 2 x + 10

4 x^{3} - 12 x - 2 x + 10

Solution

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Evaluate

- 12 x - 2 x

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

(- 12 - 2) x

Subtract the numbers

- 14 x

4 x^{3} - 14 x + 10

Show Solution

Factor the expression

Factor

2 (x - 1) (2 x^{2} + 2 x - 5)

Evaluate

4 x (x^{2} - 3) - 2 (x - 5)

Simplify

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Evaluate

4 x (x^{2} - 3)

Apply the distributive property

4 x \times x^{2} + 4 x (- 3)

Multiply the terms

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Evaluate

x \times x^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{1 + 2}

Add the numbers

x^{3}

4 x^{3} + 4 x (- 3)

Multiply the terms

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Evaluate

4 (- 3)

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

- 4 \times 3

Multiply the numbers

- 12

4 x^{3} - 12 x

4 x^{3} - 12 x - 2 (x - 5)

Simplify

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Evaluate

- 2 (x - 5)

Apply the distributive property

- 2 x - 2 (- 5)

Multiply the terms

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Evaluate

- 2 (- 5)

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

2 \times 5

Multiply the numbers

10

- 2 x + 10

4 x^{3} - 12 x - 2 x + 10

Subtract the terms

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Evaluate

- 12 x - 2 x

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

(- 12 - 2) x

Subtract the numbers

- 14 x

4 x^{3} - 14 x + 10

Rewrite the expression

2 \times 2 x^{3} - 2 \times 7 x + 2 \times 5

Factor out 2 from the expression

2 (2 x^{3} - 7 x + 5)

Solution

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Evaluate

2 x^{3} - 7 x + 5

Calculate

2 x^{3} + 2 x^{2} - 5 x - 2 x^{2} - 2 x + 5

Rewrite the expression

x \times 2 x^{2} + x \times 2 x - x \times 5 - 2 x^{2} - 2 x + 5

Factor out x from the expression

x (2 x^{2} + 2 x - 5) - 2 x^{2} - 2 x + 5

Factor out - 1 from the expression

x (2 x^{2} + 2 x - 5) - (2 x^{2} + 2 x - 5)

Factor out 2 x^{2} + 2 x - 5 from the expression

(x - 1) (2 x^{2} + 2 x - 5)

2 (x - 1) (2 x^{2} + 2 x - 5)

Show Solution

Find the roots

Find the roots of the algebra expression

x_{1} = - \frac{1 + 11}{2}, x_{2} = 1, x_{3} = \frac{- 1 + 11}{2}

Alternative Form

x_{1} \approx - 2.158312, x_{2} = 1, x_{3} \approx 1.158312

Evaluate

4 x (x^{2} - 3) - 2 (x - 5)

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

4 x (x^{2} - 3) - 2 (x - 5) = 0

Calculate

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Evaluate

4 x (x^{2} - 3) - 2 (x - 5)

Expand the expression

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Calculate

4 x (x^{2} - 3)

Apply the distributive property

4 x \times x^{2} - 4 x \times 3

Multiply the terms

4 x^{3} - 4 x \times 3

Multiply the numbers

4 x^{3} - 12 x

4 x^{3} - 12 x - 2 (x - 5)

Expand the expression

More Steps

Calculate

- 2 (x - 5)

Apply the distributive property

- 2 x - (- 2 \times 5)

Multiply the numbers

- 2 x - (- 10)

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

- 2 x + 10

4 x^{3} - 12 x - 2 x + 10

Subtract the terms

More Steps

Evaluate

- 12 x - 2 x

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

(- 12 - 2) x

Subtract the numbers

- 14 x

4 x^{3} - 14 x + 10

4 x^{3} - 14 x + 10 = 0

Factor the expression

2 (x - 1) (2 x^{2} + 2 x - 5) = 0

Divide both sides

(x - 1) (2 x^{2} + 2 x - 5) = 0

Separate the equation into 2 possible cases

x - 1 = 0 2 x^{2} + 2 x - 5 = 0

Solve the equation

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Evaluate

x - 1 = 0

Move the constant to the right-hand side and change its sign

x = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

x = 1

x = 1 2 x^{2} + 2 x - 5 = 0

Solve the equation

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Evaluate

2 x^{2} + 2 x - 5 = 0

Substitute a= 2,b= 2 and c= - 5 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{- 2 \pm 2 ^{2} - 4 \times 2 ( - 5 )}{2 \times 2}

Simplify the expression

x = \frac{- 2 \pm 2 ^{2} - 4 \times 2 ( - 5 )}{4}

Simplify the expression

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Evaluate

2^{2} - 4 \times 2 (- 5)

Multiply

2^{2} - (- 40)

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

2^{2} + 40

Evaluate the power

4 + 40

Add the numbers

44

x = \frac{- 2 \pm 44}{4}

Simplify the radical expression

More Steps

Evaluate

44

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

4 \times 11

Write the number in exponential form with the base of 2

2^{2} \times 11

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

2^{2} \times 11

Reduce the index of the radical and exponent with 2

211

x = \frac{- 2 \pm 2 11}{4}

Separate the equation into 2 possible cases

x = \frac{- 2 + 2 11}{4} x = \frac{- 2 - 2 11}{4}

Simplify the expression

x = \frac{- 1 + 11}{2} x = \frac{- 2 - 2 11}{4}

Simplify the expression

x = \frac{- 1 + 11}{2} x = - \frac{1 + 11}{2}

x = 1 x = \frac{- 1 + 11}{2} x = - \frac{1 + 11}{2}

Solution

x_{1} = - \frac{1 + 11}{2}, x_{2} = 1, x_{3} = \frac{- 1 + 11}{2}

Alternative Form

x_{1} \approx - 2.158312, x_{2} = 1, x_{3} \approx 1.158312

Show Solution

4x(x^2 3) 2(x 5)

Simplify the expression

Solution

Factor the expression

Factor

Find the roots

Find the roots of the algebra expression