Pre-Algebra Examples

${(8 - x)}^{2} = 11$

Step 1

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$8 - x = \pm \sqrt{11}$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

Tap for more steps...

Step 2.1

First, use the positive value of the $\pm$ to find the first solution.

$8 - x = \sqrt{11}$

Step 2.2

Subtract $8$ from both sides of the equation.

$- x = \sqrt{11} - 8$

Step 2.3

Divide each term in $- x = \sqrt{11} - 8$ by $- 1$ and simplify.

Tap for more steps...

Step 2.3.1

Divide each term in $- x = \sqrt{11} - 8$ by $- 1$ .

$\frac{- x}{- 1} = \frac{\sqrt{11}}{- 1} + \frac{- 8}{- 1}$

Step 2.3.2

Simplify the left side.

Tap for more steps...

Step 2.3.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{\sqrt{11}}{- 1} + \frac{- 8}{- 1}$

Step 2.3.2.2

Divide $x$ by $1$ .

$x = \frac{\sqrt{11}}{- 1} + \frac{- 8}{- 1}$

Step 2.3.3

Simplify the right side.

Tap for more steps...

Step 2.3.3.1

Simplify each term.

Tap for more steps...

Step 2.3.3.1.1

Move the negative one from the denominator of $\frac{\sqrt{11}}{- 1}$ .

$x = - 1 \cdot \sqrt{11} + \frac{- 8}{- 1}$

Step 2.3.3.1.2

Rewrite $- 1 \cdot \sqrt{11}$ as $- \sqrt{11}$ .

$x = - \sqrt{11} + \frac{- 8}{- 1}$

Step 2.3.3.1.3

Divide $- 8$ by $- 1$ .

$x = - \sqrt{11} + 8$

Step 2.4

Next, use the negative value of the $\pm$ to find the second solution.

$8 - x = - \sqrt{11}$

Step 2.5

Subtract $8$ from both sides of the equation.

$- x = - \sqrt{11} - 8$

Step 2.6

Divide each term in $- x = - \sqrt{11} - 8$ by $- 1$ and simplify.

Tap for more steps...

Step 2.6.1

Divide each term in $- x = - \sqrt{11} - 8$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- \sqrt{11}}{- 1} + \frac{- 8}{- 1}$

Step 2.6.2

Simplify the left side.

Tap for more steps...

Step 2.6.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- \sqrt{11}}{- 1} + \frac{- 8}{- 1}$

Step 2.6.2.2

Divide $x$ by $1$ .

$x = \frac{- \sqrt{11}}{- 1} + \frac{- 8}{- 1}$

Step 2.6.3

Simplify the right side.

Tap for more steps...

Step 2.6.3.1

Simplify each term.

Tap for more steps...

Step 2.6.3.1.1

Dividing two negative values results in a positive value.

$x = \frac{\sqrt{11}}{1} + \frac{- 8}{- 1}$

Step 2.6.3.1.2

Divide $\sqrt{11}$ by $1$ .

$x = \sqrt{11} + \frac{- 8}{- 1}$

Step 2.6.3.1.3

Divide $- 8$ by $- 1$ .

$x = \sqrt{11} + 8$

Step 2.7

The complete solution is the result of both the positive and negative portions of the solution.

$x = - \sqrt{11} + 8, \sqrt{11} + 8$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \sqrt{11} + 8, \sqrt{11} + 8$

Decimal Form:

$x = 4.68337520 \dots, 11.31662479 \dots$