Algebra Examples

${(x - 14)}^{2} + 13 = 12$

Step 1

Subtract $13$ from both sides of the equation.

${(x - 14)}^{2} = 12 - 13$

Step 2

Subtract $13$ from $12$ .

${(x - 14)}^{2} = - 1$

Step 3

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

$x - 14 = \pm \sqrt{- 1}$

Step 4

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

$x - 14 = \pm i$

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.

$x - 14 = i$

Step 5.2

Move all terms not containing $x$ to the right side of the equation.

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Step 5.2.1

Add $14$ to both sides of the equation.

$x = i + 14$

Step 5.2.2

Reorder $i$ and $14$ .

$x = 14 + i$

Step 5.3

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

$x - 14 = - i$

Step 5.4

Move all terms not containing $x$ to the right side of the equation.

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Step 5.4.1

Add $14$ to both sides of the equation.

$x = - i + 14$

Step 5.4.2

Reorder $- i$ and $14$ .

$x = 14 - i$

Step 5.5

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

$x = 14 + i, 14 - i$