Solve 54(x-3)^3/63(3-x)^2

Question

Simplify the expression

\frac{6 x ^{5} - 90 x ^{4} + 540 x ^{3} - 1620 x ^{2} + 2430 x - 1458}{7}

Evaluate

(54 \times \frac{( x - 3 ) ^{3}}{63}) (3 - x)^{2}

Remove the parentheses

54 \times \frac{( x - 3 ) ^{3}}{63} (3 - x)^{2}

Multiply the terms

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Multiply the terms

54 \times \frac{( x - 3 ) ^{3}}{63}

Cancel out the common factor 9

6 \times \frac{( x - 3 ) ^{3}}{7}

Multiply the terms

\frac{6 ( x - 3 ) ^{3}}{7}

\frac{6 ( x - 3 ) ^{3}}{7} (3 - x)^{2}

Multiply the terms

\frac{6 ( x - 3 ) ^{3} ( 3 - x ) ^{2}}{7}

Calculate

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Evaluate

6 (x - 3)^{3} (3 - x)^{2}

Rewrite the expression

6 (- 1)^{2} (x - 3)^{5}

Multiply the terms

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Evaluate

6 (- 1)^{2}

Evaluate the power

6 \times 1

Multiply the numbers

6

6 (x - 3)^{5}

\frac{6 ( x - 3 ) ^{5}}{7}

Solution

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Evaluate

6 (x - 3)^{5}

Expand the expression

6 (x^{5} - 15 x^{4} + 90 x^{3} - 270 x^{2} + 405 x - 243)

Apply the distributive property

6 x^{5} - 6 \times 15 x^{4} + 6 \times 90 x^{3} - 6 \times 270 x^{2} + 6 \times 405 x - 6 \times 243

Multiply the numbers

6 x^{5} - 90 x^{4} + 6 \times 90 x^{3} - 6 \times 270 x^{2} + 6 \times 405 x - 6 \times 243

Multiply the numbers

6 x^{5} - 90 x^{4} + 540 x^{3} - 6 \times 270 x^{2} + 6 \times 405 x - 6 \times 243

Multiply the numbers

6 x^{5} - 90 x^{4} + 540 x^{3} - 1620 x^{2} + 6 \times 405 x - 6 \times 243

Multiply the numbers

6 x^{5} - 90 x^{4} + 540 x^{3} - 1620 x^{2} + 2430 x - 6 \times 243

Multiply the numbers

6 x^{5} - 90 x^{4} + 540 x^{3} - 1620 x^{2} + 2430 x - 1458

\frac{6 x ^{5} - 90 x ^{4} + 540 x ^{3} - 1620 x ^{2} + 2430 x - 1458}{7}

Show Solution

Find the roots

x = 3

Evaluate

(54 \times \frac{( x - 3 ) ^{3}}{63}) (3 - x)^{2}

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

(54 \times \frac{( x - 3 ) ^{3}}{63}) (3 - x)^{2} = 0

Multiply the terms

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Multiply the terms

54 \times \frac{( x - 3 ) ^{3}}{63}

Cancel out the common factor 9

6 \times \frac{( x - 3 ) ^{3}}{7}

Multiply the terms

\frac{6 ( x - 3 ) ^{3}}{7}

\frac{6 ( x - 3 ) ^{3}}{7} (3 - x)^{2} = 0

Multiply the terms

\frac{6 ( x - 3 ) ^{3} ( 3 - x ) ^{2}}{7} = 0

Simplify

6 (x - 3)^{3} (3 - x)^{2} = 0

Elimination the left coefficient

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

Separate the equation into 2 possible cases

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

Solve the equation

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Evaluate

(x - 3)^{3} = 0

The only way a power can be 0 is when the base equals 0

x - 3 = 0

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

x = 0 + 3

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

x = 3

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

Solve the equation

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Evaluate

(3 - x)^{2} = 0

The only way a power can be 0 is when the base equals 0

3 - x = 0

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

- x = 0 - 3

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

- x = - 3

Change the signs on both sides of the equation

x = 3

x = 3 x = 3

Solution

x = 3

Show Solution