Pre-Algebra Examples

${(u - 6)}^{2} + 56 = 0$

Step 1

Subtract $56$ from both sides of the equation.

${(u - 6)}^{2} = - 56$

Step 2

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

$u - 6 = \pm \sqrt{- 56}$

Step 3

Simplify $\pm \sqrt{- 56}$ .

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Step 3.1

Rewrite $- 56$ as $- 1 (56)$ .

$u - 6 = \pm \sqrt{- 1 (56)}$

Step 3.2

Rewrite $\sqrt{- 1 (56)}$ as $\sqrt{- 1} \cdot \sqrt{56}$ .

$u - 6 = \pm \sqrt{- 1} \cdot \sqrt{56}$

Step 3.3

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

$u - 6 = \pm i \cdot \sqrt{56}$

Step 3.4

Rewrite $56$ as $2^{2} \cdot 14$ .

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Step 3.4.1

Factor $4$ out of $56$ .

$u - 6 = \pm i \cdot \sqrt{4 (14)}$

Step 3.4.2

Rewrite $4$ as $2^{2}$ .

$u - 6 = \pm i \cdot \sqrt{2^{2} \cdot 14}$

Step 3.5

Pull terms out from under the radical.

$u - 6 = \pm i \cdot (2 \sqrt{14})$

Step 3.6

Move $2$ to the left of $i$ .

$u - 6 = \pm 2 i \sqrt{14}$

Step 4

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

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Step 4.1

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

$u - 6 = 2 i \sqrt{14}$

Step 4.2

Add $6$ to both sides of the equation.

$u = 2 i \sqrt{14} + 6$

Step 4.3

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

$u - 6 = - 2 i \sqrt{14}$

Step 4.4

Add $6$ to both sides of the equation.

$u = - 2 i \sqrt{14} + 6$

Step 4.5

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

$u = 2 i \sqrt{14} + 6, - 2 i \sqrt{14} + 6$