Precalculus Examples

${(2 x + 7)}^{2} = 25$

Step 1

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

$2 x + 7 = \pm \sqrt{25}$

Step 2

Simplify $\pm \sqrt{25}$ .

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Step 2.1

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

$2 x + 7 = \pm \sqrt{5^{2}}$

Step 2.2

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

$2 x + 7 = \pm 5$

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.

$2 x + 7 = 5$

Step 3.2

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

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Step 3.2.1

Subtract $7$ from both sides of the equation.

$2 x = 5 - 7$

Step 3.2.2

Subtract $7$ from $5$ .

$2 x = - 2$

Step 3.3

Divide each term in $2 x = - 2$ by $2$ and simplify.

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Step 3.3.1

Divide each term in $2 x = - 2$ by $2$ .

$\frac{2 x}{2} = \frac{- 2}{2}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $2$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 2}{2}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 2}{2}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 2$ by $2$ .

$x = - 1$

Step 3.4

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

$2 x + 7 = - 5$

Step 3.5

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

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Step 3.5.1

Subtract $7$ from both sides of the equation.

$2 x = - 5 - 7$

Step 3.5.2

Subtract $7$ from $- 5$ .

$2 x = - 12$

Step 3.6

Divide each term in $2 x = - 12$ by $2$ and simplify.

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Step 3.6.1

Divide each term in $2 x = - 12$ by $2$ .

$\frac{2 x}{2} = \frac{- 12}{2}$

Step 3.6.2

Simplify the left side.

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Step 3.6.2.1

Cancel the common factor of $2$ .

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Step 3.6.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 12}{2}$

Step 3.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 12}{2}$

Step 3.6.3

Simplify the right side.

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Step 3.6.3.1

Divide $- 12$ by $2$ .

$x = - 6$

Step 3.7

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

$x = - 1, - 6$