Algebra Examples

$2 {(x - 7)}^{2} = 2$

Step 1

Divide each term in $2 {(x - 7)}^{2} = 2$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 {(x - 7)}^{2} = 2$ by $2$ .

$\frac{2 {(x - 7)}^{2}}{2} = \frac{2}{2}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 {(x - 7)}^{2}}{2} = \frac{2}{2}$

Step 1.2.1.2

Divide ${(x - 7)}^{2}$ by $1$ .

${(x - 7)}^{2} = \frac{2}{2}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $2$ by $2$ .

${(x - 7)}^{2} = 1$

Step 2

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

$x - 7 = \pm \sqrt{1}$

Step 3

Any root of $1$ is $1$ .

$x - 7 = \pm 1$

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.

$x - 7 = 1$

Step 4.2

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

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Step 4.2.1

Add $7$ to both sides of the equation.

$x = 1 + 7$

Step 4.2.2

Add $1$ and $7$ .

$x = 8$

Step 4.3

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

$x - 7 = - 1$

Step 4.4

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

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Step 4.4.1

Add $7$ to both sides of the equation.

$x = - 1 + 7$

Step 4.4.2

Add $- 1$ and $7$ .

$x = 6$

Step 4.5

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

$x = 8, 6$