Solve x^26x 9x^2-9

Question

Simplify the expression

54 x^{5} - 9

Evaluate

x^{2} \times 6 x \times 9 x^{2} - 9

Solution

More Steps

Evaluate

x^{2} \times 6 x \times 9 x^{2}

Multiply the terms with the same base by adding their exponents

x^{2 + 1 + 2} \times 6 \times 9

Add the numbers

x^{5} \times 6 \times 9

Multiply the terms

x^{5} \times 54

Use the commutative property to reorder the terms

54 x^{5}

54 x^{5} - 9

Show Solution

Factor the expression

9 (6 x^{5} - 1)

Evaluate

x^{2} \times 6 x \times 9 x^{2} - 9

Multiply

More Steps

Evaluate

x^{2} \times 6 x \times 9 x^{2}

Multiply the terms with the same base by adding their exponents

x^{2 + 1 + 2} \times 6 \times 9

Add the numbers

x^{5} \times 6 \times 9

Multiply the terms

x^{5} \times 54

Use the commutative property to reorder the terms

54 x^{5}

54 x^{5} - 9

Solution

9 (6 x^{5} - 1)

Show Solution

Find the roots

x = \frac{5 1296}{6}

Alternative Form

x \approx 0.698827

Evaluate

x^{2} \times 6 x \times 9 x^{2} - 9

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

x^{2} \times 6 x \times 9 x^{2} - 9 = 0

Multiply

More Steps

Multiply the terms

x^{2} \times 6 x \times 9 x^{2}

Multiply the terms with the same base by adding their exponents

x^{2 + 1 + 2} \times 6 \times 9

Add the numbers

x^{5} \times 6 \times 9

Multiply the terms

x^{5} \times 54

Use the commutative property to reorder the terms

54 x^{5}

54 x^{5} - 9 = 0

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

54 x^{5} = 0 + 9

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

54 x^{5} = 9

Divide both sides

\frac{54 x ^{5}}{54} = \frac{9}{54}

Divide the numbers

x^{5} = \frac{9}{54}

Cancel out the common factor 9

x^{5} = \frac{1}{6}

Take the 5 -th root on both sides of the equation

5 x^{5} = 5 \frac{1}{6}

Calculate

x = 5 \frac{1}{6}

Solution

More Steps

Evaluate

5 \frac{1}{6}

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

\frac{5 1}{5 6}

Simplify the radical expression

\frac{1}{5 6}

Multiply by the Conjugate

\frac{5 6 ^{4}}{5 6 \times 5 6 ^{4}}

Simplify

\frac{5 1296}{5 6 \times 5 6 ^{4}}

Multiply the numbers

More Steps

Evaluate

56 \times 5 6^{4}

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

5 6 \times 6^{4}

Calculate the product

5 6^{5}

Reduce the index of the radical and exponent with 5

6

\frac{5 1296}{6}

x = \frac{5 1296}{6}

Alternative Form

x \approx 0.698827

Show Solution