Precalculus Examples

${(x - 1)}^{2} = 25$

Step 1

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

$x - 1 = \pm \sqrt{25}$

Step 2

Simplify $\pm \sqrt{25}$ .

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Step 2.1

Rewrite $25$ as $5^{2}$ .

$x - 1 = \pm \sqrt{5^{2}}$

Step 2.2

Pull terms out from under the radical, assuming positive real numbers.

$x - 1 = \pm 5$

Step 3

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

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Step 3.1

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

$x - 1 = 5$

Step 3.2

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

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Step 3.2.1

Add $1$ to both sides of the equation.

$x = 5 + 1$

Step 3.2.2

Add $5$ and $1$ .

$x = 6$

Step 3.3

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

$x - 1 = - 5$

Step 3.4

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

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Step 3.4.1

Add $1$ to both sides of the equation.

$x = - 5 + 1$

Step 3.4.2

Add $- 5$ and $1$ .

$x = - 4$

Step 3.5

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

$x = 6, - 4$