Solve x^4 2x^2-8 - ScanMath

Question

Simplify the expression

2 x^{6} - 8

Evaluate

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

Solution

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 2

Add the numbers

x^{6} \times 2

Use the commutative property to reorder the terms

2 x^{6}

2 x^{6} - 8

Show Solution

Factor the expression

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

Evaluate

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

Evaluate

More Steps

Evaluate

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

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 2

Add the numbers

x^{6} \times 2

Use the commutative property to reorder the terms

2 x^{6}

2 x^{6} - 8

Factor out 2 from the expression

2 (x^{6} - 4)

Solution

More Steps

Evaluate

x^{6} - 4

Rewrite the expression in exponential form

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

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

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

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

Show Solution

Find the roots

x_{1} = - 32, x_{2} = 32

Alternative Form

x_{1} \approx - 1.259921, x_{2} \approx 1.259921

Evaluate

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

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

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

Multiply

More Steps

Multiply the terms

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

Multiply the terms with the same base by adding their exponents

x^{4 + 2} \times 2

Add the numbers

x^{6} \times 2

Use the commutative property to reorder the terms

2 x^{6}

2 x^{6} - 8 = 0

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

2 x^{6} = 0 + 8

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

2 x^{6} = 8

Divide both sides

\frac{2 x ^{6}}{2} = \frac{8}{2}

Divide the numbers

x^{6} = \frac{8}{2}

Divide the numbers

More Steps

Evaluate

\frac{8}{2}

Reduce the numbers

\frac{4}{1}

Calculate

4

x^{6} = 4

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

x = \pm 64

Simplify the expression

More Steps

Evaluate

64

Write the number in exponential form with the base of 2

6 2^{2}

Reduce the index of the radical and exponent with 2

32

x = \pm 32

Separate the equation into 2 possible cases

x = 32 x = - 32

Solution

x_{1} = - 32, x_{2} = 32

Alternative Form

x_{1} \approx - 1.259921, x_{2} \approx 1.259921

Show Solution