Algebra Examples

$\frac{1}{4} {(x + 1)}^{2} - 16 = 0$

Step 1

Add $16$ to both sides of the equation.

$\frac{1}{4} \cdot {(x + 1)}^{2} = 16$

Step 2

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

$\frac{{(x + 1)}^{2}}{4} = 16$

Step 3

Multiply both sides of the equation by $4$ .

$4 \frac{{(x + 1)}^{2}}{4} = 4 \cdot 16$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Cancel the common factor of $4$ .

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Step 4.1.1.1

Cancel the common factor.

$4 \frac{{(x + 1)}^{2}}{4} = 4 \cdot 16$

Step 4.1.1.2

Rewrite the expression.

${(x + 1)}^{2} = 4 \cdot 16$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $4$ by $16$ .

${(x + 1)}^{2} = 64$

Step 5

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

$x + 1 = \pm \sqrt{64}$

Step 6

Simplify $\pm \sqrt{64}$ .

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Step 6.1

Rewrite $64$ as $8^{2}$ .

$x + 1 = \pm \sqrt{8^{2}}$

Step 6.2

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

$x + 1 = \pm 8$

Step 7

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

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Step 7.1

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

$x + 1 = 8$

Step 7.2

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

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Step 7.2.1

Subtract $1$ from both sides of the equation.

$x = 8 - 1$

Step 7.2.2

Subtract $1$ from $8$ .

$x = 7$

Step 7.3

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

$x + 1 = - 8$

Step 7.4

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

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Step 7.4.1

Subtract $1$ from both sides of the equation.

$x = - 8 - 1$

Step 7.4.2

Subtract $1$ from $- 8$ .

$x = - 9$

Step 7.5

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

$x = 7, - 9$