Solve x^48x^2 - 9

Question

Simplify the expression

8 x^{6} - 9

Evaluate

x^{4} \times 8 x^{2} - 9

Solution

More Steps

Evaluate

x^{4} \times 8 x^{2}

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 8

Add the numbers

x^{6} \times 8

Use the commutative property to reorder the terms

8 x^{6}

8 x^{6} - 9

Show Solution

x_{1} = - \frac{6 72}{2}, x_{2} = \frac{6 72}{2}

Alternative Form

x_{1} \approx - 1.019824, x_{2} \approx 1.019824

Evaluate

x^{4} \times 8 x^{2} - 9

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

x^{4} \times 8 x^{2} - 9 = 0

Multiply

More Steps

Multiply the terms

x^{4} \times 8 x^{2}

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 8

Add the numbers

x^{6} \times 8

Use the commutative property to reorder the terms

8 x^{6}

8 x^{6} - 9 = 0

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

8 x^{6} = 0 + 9

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

8 x^{6} = 9

Divide both sides

\frac{8 x ^{6}}{8} = \frac{9}{8}

Divide the numbers

x^{6} = \frac{9}{8}

Take the root of both sides of the equation and remember to use both positive and negative roots

x = \pm 6 \frac{9}{8}

Simplify the expression

More Steps

Evaluate

6 \frac{9}{8}

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

\frac{6 9}{6 8}

Simplify the radical expression

More Steps

Evaluate

69

Write the number in exponential form with the base of 3

6 3^{2}

Reduce the index of the radical and exponent with 2

33

\frac{3 3}{6 8}

Simplify the radical expression

More Steps

Evaluate

68

Write the number in exponential form with the base of 2

6 2^{3}

Reduce the index of the radical and exponent with 3

2

\frac{3 3}{2}

Multiply by the Conjugate

\frac{3 3 \times 2}{2 \times 2}

Multiply the numbers

More Steps

Evaluate

33 \times 2

Use n a = mn a^{m} to expand the expression

6 3^{2} \times 2

Use n a = mn a^{m} to expand the expression

6 3^{2} \times 6 2^{3}

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

6 3^{2} \times 2^{3}

Calculate the product

672

\frac{6 72}{2 \times 2}

When a square root of an expression is multiplied by itself,the result is that expression

\frac{6 72}{2}

x = \pm \frac{6 72}{2}

Separate the equation into 2 possible cases

x = \frac{6 72}{2} x = - \frac{6 72}{2}

Solution

x_{1} = - \frac{6 72}{2}, x_{2} = \frac{6 72}{2}

Alternative Form

x_{1} \approx - 1.019824, x_{2} \approx 1.019824

Show Solution