Algebra Examples

$2 {(x + 5)}^{2} + 37 = 39$

Step 1

Subtract $37$ from both sides of the equation.

$2 {(x + 5)}^{2} = 39 - 37$

Step 2

Subtract $37$ from $39$ .

$2 {(x + 5)}^{2} = 2$

Step 3

Divide each term in $2 {(x + 5)}^{2} = 2$ by $2$ and simplify.

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Step 3.1

Divide each term in $2 {(x + 5)}^{2} = 2$ by $2$ .

$\frac{2 {(x + 5)}^{2}}{2} = \frac{2}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $2$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{2 {(x + 5)}^{2}}{2} = \frac{2}{2}$

Step 3.2.1.2

Divide ${(x + 5)}^{2}$ by $1$ .

${(x + 5)}^{2} = \frac{2}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $2$ by $2$ .

${(x + 5)}^{2} = 1$

Step 4

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

$x + 5 = \pm \sqrt{1}$

Step 5

Any root of $1$ is $1$ .

$x + 5 = \pm 1$

Step 6

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

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Step 6.1

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

$x + 5 = 1$

Step 6.2

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

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Step 6.2.1

Subtract $5$ from both sides of the equation.

$x = 1 - 5$

Step 6.2.2

Subtract $5$ from $1$ .

$x = - 4$

Step 6.3

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

$x + 5 = - 1$

Step 6.4

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

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Step 6.4.1

Subtract $5$ from both sides of the equation.

$x = - 1 - 5$

Step 6.4.2

Subtract $5$ from $- 1$ .

$x = - 6$

Step 6.5

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

$x = - 4, - 6$