Solve (x-2)^(2) 27(x-2)-90

Question

Simplify the expression

27 x^{3} - 162 x^{2} + 324 x - 306

Evaluate

(x - 2)^{2} \times 27 (x - 2) - 90

Multiply

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Multiply the terms

(x - 2)^{2} \times 27 (x - 2)

Multiply the terms with the same base by adding their exponents

(x - 2)^{2 + 1} \times 27

Add the numbers

(x - 2)^{3} \times 27

Use the commutative property to reorder the terms

27 (x - 2)^{3}

27 (x - 2)^{3} - 90

Expand the expression

More Steps

Calculate

27 (x - 2)^{3}

Simplify

27 (x^{3} - 6 x^{2} + 12 x - 8)

Apply the distributive property

27 x^{3} - 27 \times 6 x^{2} + 27 \times 12 x - 27 \times 8

Multiply the numbers

27 x^{3} - 162 x^{2} + 27 \times 12 x - 27 \times 8

Multiply the numbers

27 x^{3} - 162 x^{2} + 324 x - 27 \times 8

Multiply the numbers

27 x^{3} - 162 x^{2} + 324 x - 216

27 x^{3} - 162 x^{2} + 324 x - 216 - 90

Solution

27 x^{3} - 162 x^{2} + 324 x - 306

Show Solution

Factor the expression

9 (3 x^{3} - 18 x^{2} + 36 x - 34)

Evaluate

(x - 2)^{2} \times 27 (x - 2) - 90

Multiply

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Evaluate

(x - 2)^{2} \times 27 (x - 2)

Multiply the terms with the same base by adding their exponents

(x - 2)^{2 + 1} \times 27

Add the numbers

(x - 2)^{3} \times 27

Use the commutative property to reorder the terms

27 (x - 2)^{3}

27 (x - 2)^{3} - 90

Simplify

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Evaluate

27 (x - 2)^{3}

Simplify

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Evaluate

(x - 2)^{3}

Use (a - b)^{3} = a^{3} - 3 a^{2} b + 3 a b^{2} - b^{3} to expand the expression

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

Calculate

x^{3} - 6 x^{2} + 12 x - 8

27 (x^{3} - 6 x^{2} + 12 x - 8)

Apply the distributive property

27 x^{3} + 27 (- 6 x^{2}) + 27 \times 12 x + 27 (- 8)

Multiply the terms

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Evaluate

27 (- 6)

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

- 27 \times 6

Multiply the numbers

- 162

27 x^{3} - 162 x^{2} + 27 \times 12 x + 27 (- 8)

Multiply the terms

27 x^{3} - 162 x^{2} + 324 x + 27 (- 8)

Multiply the terms

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Evaluate

27 (- 8)

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

- 27 \times 8

Multiply the numbers

- 216

27 x^{3} - 162 x^{2} + 324 x - 216

27 x^{3} - 162 x^{2} + 324 x - 216 - 90

Subtract the numbers

27 x^{3} - 162 x^{2} + 324 x - 306

Solution

9 (3 x^{3} - 18 x^{2} + 36 x - 34)

Show Solution

Find the roots

x = \frac{3 90 + 6}{3}

Alternative Form

x \approx 3.493802

Evaluate

(x - 2)^{2} \times 27 (x - 2) - 90

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

(x - 2)^{2} \times 27 (x - 2) - 90 = 0

Multiply

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Multiply the terms

(x - 2)^{2} \times 27 (x - 2)

Multiply the terms with the same base by adding their exponents

(x - 2)^{2 + 1} \times 27

Add the numbers

(x - 2)^{3} \times 27

Use the commutative property to reorder the terms

27 (x - 2)^{3}

27 (x - 2)^{3} - 90 = 0

Add or subtract both sides

27 (x - 2)^{3} = 0 + 90

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

27 (x - 2)^{3} = 90

Divide both sides

\frac{27 ( x - 2 ) ^{3}}{27} = \frac{90}{27}

Divide the numbers

(x - 2)^{3} = \frac{90}{27}

Cancel out the common factor 9

(x - 2)^{3} = \frac{10}{3}

Take the 3 -th root on both sides of the equation

3 (x - 2)^{3} = 3 \frac{10}{3}

Calculate

x - 2 = 3 \frac{10}{3}

Simplify the root

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Evaluate

3 \frac{10}{3}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 10}{3 3}

Multiply by the Conjugate

\frac{3 10 \times 3 3 ^{2}}{3 3 \times 3 3 ^{2}}

Simplify

\frac{3 10 \times 3 9}{3 3 \times 3 3 ^{2}}

Multiply the numbers

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Evaluate

310 \times 39

The product of roots with the same index is equal to the root of the product

3 10 \times 9

Calculate the product

390

\frac{3 90}{3 3 \times 3 3 ^{2}}

Multiply the numbers

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Evaluate

33 \times 3 3^{2}

The product of roots with the same index is equal to the root of the product

3 3 \times 3^{2}

Calculate the product

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{3 90}{3}

x - 2 = \frac{3 90}{3}

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

x = \frac{3 90}{3} + 2

Solution

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Evaluate

\frac{3 90}{3} + 2

Reduce fractions to a common denominator

\frac{3 90}{3} + \frac{2 \times 3}{3}

Write all numerators above the common denominator

\frac{3 90 + 2 \times 3}{3}

Multiply the numbers

\frac{3 90 + 6}{3}

x = \frac{3 90 + 6}{3}

Alternative Form

x \approx 3.493802

Show Solution