Pre-Algebra Examples

${(x - 5)}^{2} + 10 = 4$

Step 1

Subtract $10$ from both sides of the equation.

${(x - 5)}^{2} = 4 - 10$

Step 2

Subtract $10$ from $4$ .

${(x - 5)}^{2} = - 6$

Step 3

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

$x - 5 = \pm \sqrt{- 6}$

Step 4

Simplify $\pm \sqrt{- 6}$ .

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Step 4.1

Rewrite $- 6$ as $- 1 (6)$ .

$x - 5 = \pm \sqrt{- 1 (6)}$

Step 4.2

Rewrite $\sqrt{- 1 (6)}$ as $\sqrt{- 1} \cdot \sqrt{6}$ .

$x - 5 = \pm \sqrt{- 1} \cdot \sqrt{6}$

Step 4.3

Rewrite $\sqrt{- 1}$ as $i$ .

$x - 5 = \pm i \sqrt{6}$

Step 5

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

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Step 5.1

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

$x - 5 = i \sqrt{6}$

Step 5.2

Add $5$ to both sides of the equation.

$x = i \sqrt{6} + 5$

Step 5.3

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

$x - 5 = - i \sqrt{6}$

Step 5.4

Add $5$ to both sides of the equation.

$x = - i \sqrt{6} + 5$

Step 5.5

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

$x = i \sqrt{6} + 5, - i \sqrt{6} + 5$