Solve 8x^4 -2 - ScanMath

Question

Factor the expression

2 (2 x^{2} - 1) (2 x^{2} + 1)

Evaluate

8 x^{4} - 2

Factor out 2 from the expression

2 (4 x^{4} - 1)

Solution

More Steps

Evaluate

4 x^{4} - 1

Rewrite the expression in exponential form

(2 x^{2})^{2} - 1^{2}

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

(2 x^{2} - 1) (2 x^{2} + 1)

2 (2 x^{2} - 1) (2 x^{2} + 1)

Show Solution

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

Alternative Form

x_{1} \approx - 0.707107, x_{2} \approx 0.707107

Evaluate

8 x^{4} - 2

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

8 x^{4} - 2 = 0

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

8 x^{4} = 0 + 2

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

8 x^{4} = 2

Divide both sides

\frac{8 x ^{4}}{8} = \frac{2}{8}

Divide the numbers

x^{4} = \frac{2}{8}

Cancel out the common factor 2

x^{4} = \frac{1}{4}

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

x = \pm 4 \frac{1}{4}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{4}

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

\frac{4 1}{4 4}

Simplify the radical expression

\frac{1}{4 4}

Simplify the radical expression

More Steps

Evaluate

44

Write the number in exponential form with the base of 2

4 2^{2}

Reduce the index of the radical and exponent with 2

2

\frac{1}{2}

Multiply by the Conjugate

\frac{2}{2 \times 2}

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

\frac{2}{2}

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

Separate the equation into 2 possible cases

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

Solution

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

Alternative Form

x_{1} \approx - 0.707107, x_{2} \approx 0.707107

Show Solution