Solve 8x^6-27 - ScanMath

Question

Factor the expression

(2 x^{2} - 3) (4 x^{4} + 6 x^{2} + 9)

Evaluate

8 x^{6} - 27

Rewrite the expression in exponential form

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

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

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

Evaluate

More Steps

Evaluate

(2 x^{2})^{2}

To raise a product to a power,raise each factor to that power

2^{2} (x^{2})^{2}

Evaluate the power

4 (x^{2})^{2}

Evaluate the power

More Steps

Evaluate

(x^{2})^{2}

Multiply the exponents

x^{2 \times 2}

Multiply the terms

x^{4}

4 x^{4}

(2 x^{2} - 3) (4 x^{4} + 2 x^{2} \times 3 + 3^{2})

Evaluate

(2 x^{2} - 3) (4 x^{4} + 6 x^{2} + 3^{2})

Solution

(2 x^{2} - 3) (4 x^{4} + 6 x^{2} + 9)

Show Solution

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

Alternative Form

x_{1} \approx - 1.224745, x_{2} \approx 1.224745

Evaluate

8 x^{6} - 27

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

8 x^{6} - 27 = 0

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

8 x^{6} = 0 + 27

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

8 x^{6} = 27

Divide both sides

\frac{8 x ^{6}}{8} = \frac{27}{8}

Divide the numbers

x^{6} = \frac{27}{8}

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

x = \pm 6 \frac{27}{8}

Simplify the expression

More Steps

Evaluate

6 \frac{27}{8}

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

\frac{6 27}{6 8}

Simplify the radical expression

More Steps

Evaluate

627

Write the number in exponential form with the base of 3

6 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{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}{2}

Multiply by the Conjugate

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

Multiply the numbers

More Steps

Evaluate

3 \times 2

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

3 \times 2

Calculate the product

6

\frac{6}{2 \times 2}

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

\frac{6}{2}

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

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

x_{1} \approx - 1.224745, x_{2} \approx 1.224745

Show Solution