Pre-Algebra Examples

$\sqrt{2 x} = - 8$

Step 1

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{2 x}}^{2} = {(- 8)}^{2}$

Step 2

Simplify each side of the equation.

Tap for more steps...

Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 x}$ as ${(2 x)}^{\frac{1}{2}}$ .

${({(2 x)}^{\frac{1}{2}})}^{2} = {(- 8)}^{2}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify ${({(2 x)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 2.2.1.1

Multiply the exponents in ${({(2 x)}^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 2.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(2 x)}^{\frac{1}{2} \cdot 2} = {(- 8)}^{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1.2.1

Cancel the common factor.

${(2 x)}^{\frac{1}{2} \cdot 2} = {(- 8)}^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

${(2 x)}^{1} = {(- 8)}^{2}$

Step 2.2.1.2

Simplify.

$2 x = {(- 8)}^{2}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Raise $- 8$ to the power of $2$ .

$2 x = 64$

Step 3

Divide each term in $2 x = 64$ by $2$ and simplify.

Tap for more steps...

Step 3.1

Divide each term in $2 x = 64$ by $2$ .

$\frac{2 x}{2} = \frac{64}{2}$

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{64}{2}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{64}{2}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

Divide $64$ by $2$ .

$x = 32$

Step 4

Exclude the solutions that do not make $\sqrt{2 x} = - 8$ true.

$No solution$