Solve (a-3 (a-3) (a-3))

Question

Simplify the expression

19 a - 3 a^{2} - 27

Evaluate

a - 3 (a - 3) (a - 3)

Multiply the terms

a - 3 (a - 3)^{2}

Expand the expression

More Steps

Calculate

- 3 (a - 3)^{2}

Simplify

- 3 (a^{2} - 6 a + 9)

Apply the distributive property

- 3 a^{2} - (- 3 \times 6 a) - 3 \times 9

Multiply the numbers

- 3 a^{2} - (- 18 a) - 3 \times 9

Multiply the numbers

- 3 a^{2} - (- 18 a) - 27

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

- 3 a^{2} + 18 a - 27

a - 3 a^{2} + 18 a - 27

Solution

More Steps

Evaluate

a + 18 a

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

(1 + 18) a

Add the numbers

19 a

19 a - 3 a^{2} - 27

Show Solution

Find the roots

a_{1} = \frac{19 - 37}{6}, a_{2} = \frac{19 + 37}{6}

Alternative Form

a_{1} \approx 2.152873, a_{2} \approx 4.18046

Evaluate

(a - 3 (a - 3) (a - 3))

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

a - 3 (a - 3) (a - 3) = 0

Multiply the terms

a - 3 (a - 3)^{2} = 0

Subtract the terms

More Steps

Simplify

a - 3 (a - 3)^{2}

Expand the expression

More Steps

Calculate

- 3 (a - 3)^{2}

Simplify

- 3 (a^{2} - 6 a + 9)

Apply the distributive property

- 3 a^{2} - (- 3 \times 6 a) - 3 \times 9

Multiply the numbers

- 3 a^{2} - (- 18 a) - 3 \times 9

Multiply the numbers

- 3 a^{2} - (- 18 a) - 27

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

- 3 a^{2} + 18 a - 27

a - 3 a^{2} + 18 a - 27

Add the terms

More Steps

Evaluate

a + 18 a

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

(1 + 18) a

Add the numbers

19 a

19 a - 3 a^{2} - 27

19 a - 3 a^{2} - 27 = 0

Rewrite in standard form

- 3 a^{2} + 19 a - 27 = 0

Multiply both sides

3 a^{2} - 19 a + 27 = 0

Substitute a= 3,b= - 19 and c= 27 into the quadratic formula a = \frac{- b \pm b ^{2} - 4 a c}{2 a}

a = \frac{19 \pm ( - 19 ) ^{2} - 4 \times 3 \times 27}{2 \times 3}

Simplify the expression

a = \frac{19 \pm ( - 19 ) ^{2} - 4 \times 3 \times 27}{6}

Simplify the expression

More Steps

Evaluate

(- 19)^{2} - 4 \times 3 \times 27

Multiply the terms

More Steps

Multiply the terms

4 \times 3 \times 27

Multiply the terms

12 \times 27

Multiply the numbers

324

(- 19)^{2} - 324

Rewrite the expression

1 9^{2} - 324

Evaluate the power

361 - 324

Subtract the numbers

37

a = \frac{19 \pm 37}{6}

Separate the equation into 2 possible cases

a = \frac{19 + 37}{6} a = \frac{19 - 37}{6}

Solution

a_{1} = \frac{19 - 37}{6}, a_{2} = \frac{19 + 37}{6}

Alternative Form

a_{1} \approx 2.152873, a_{2} \approx 4.18046

Show Solution