Algebra Examples

$\sqrt{x} = - 8 + 2 \sqrt{x}$

Step 1

Solve for $\sqrt{x}$ .

Tap for more steps...

Step 1.1

Move all terms containing $\sqrt{x}$ to the left side of the equation.

Tap for more steps...

Step 1.1.1

Subtract $2 \sqrt{x}$ from both sides of the equation.

$\sqrt{x} - 2 \sqrt{x} = - 8$

Step 1.1.2

Subtract $2 \sqrt{x}$ from $\sqrt{x}$ .

$- \sqrt{x} = - 8$

Step 1.2

Divide each term in $- \sqrt{x} = - 8$ by $- 1$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $- \sqrt{x} = - 8$ by $- 1$ .

$\frac{- \sqrt{x}}{- 1} = \frac{- 8}{- 1}$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Dividing two negative values results in a positive value.

$\frac{\sqrt{x}}{1} = \frac{- 8}{- 1}$

Step 1.2.2.2

Divide $\sqrt{x}$ by $1$ .

$\sqrt{x} = \frac{- 8}{- 1}$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Divide $- 8$ by $- 1$ .

$\sqrt{x} = 8$

Step 2

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

${\sqrt{x}}^{2} = 8^{2}$

Step 3

Simplify each side of the equation.

Tap for more steps...

Step 3.1

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

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

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

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

Tap for more steps...

Step 3.2.1.1

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

Tap for more steps...

Step 3.2.1.1.1

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

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

Step 3.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1.1.2.1

Cancel the common factor.

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

Step 3.2.1.1.2.2

Rewrite the expression.

$x^{1} = 8^{2}$

Step 3.2.1.2

Simplify.

$x = 8^{2}$

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

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

$x = 64$