Algebra Examples

$\frac{1}{2} {(x - 4)}^{2} = 8$

Step 1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot {(x - 4)}^{2}) = 2 \cdot 8$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $2 (\frac{1}{2} \cdot {(x - 4)}^{2})$ .

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Step 2.1.1.1

Combine $\frac{1}{2}$ and ${(x - 4)}^{2}$ .

$2 \frac{{(x - 4)}^{2}}{2} = 2 \cdot 8$

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Cancel the common factor.

$2 \frac{{(x - 4)}^{2}}{2} = 2 \cdot 8$

Step 2.1.1.2.2

Rewrite the expression.

${(x - 4)}^{2} = 2 \cdot 8$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $2$ by $8$ .

${(x - 4)}^{2} = 16$

Step 3

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

$x - 4 = \pm \sqrt{16}$

Step 4

Simplify $\pm \sqrt{16}$ .

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Step 4.1

Rewrite $16$ as $4^{2}$ .

$x - 4 = \pm \sqrt{4^{2}}$

Step 4.2

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

$x - 4 = \pm 4$

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.

$x - 4 = 4$

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 $4$ to both sides of the equation.

$x = 4 + 4$

Step 5.2.2

Add $4$ and $4$ .

$x = 8$

Step 5.3

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

$x - 4 = - 4$

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 $4$ to both sides of the equation.

$x = - 4 + 4$

Step 5.4.2

Add $- 4$ and $4$ .

$x = 0$

Step 5.5

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

$x = 8, 0$