Solve Using the Square Root Property 9(x+1)^2=16

$9 {(x + 1)}^{2} = 16$

Step 1

Divide each term in $9 {(x + 1)}^{2} = 16$ by $9$ and simplify.

Divide each term in $9 {(x + 1)}^{2} = 16$ by $9$ .

$\frac{9 {(x + 1)}^{2}}{9} = \frac{16}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 {(x + 1)}^{2}}{9} = \frac{16}{9}$

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

${(x + 1)}^{2} = \frac{16}{9}$

Step 2

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

$x + 1 = \pm \sqrt{\frac{16}{9}}$

Step 3

Simplify $\pm \sqrt{\frac{16}{9}}$ .

Rewrite $\sqrt{\frac{16}{9}}$ as $\frac{\sqrt{16}}{\sqrt{9}}$ .

$x + 1 = \pm \frac{\sqrt{16}}{\sqrt{9}}$

Simplify the numerator.

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

$x + 1 = \pm \frac{\sqrt{4^{2}}}{\sqrt{9}}$

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

$x + 1 = \pm \frac{4}{\sqrt{9}}$

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

$x + 1 = \pm \frac{4}{\sqrt{3^{2}}}$

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

$x + 1 = \pm \frac{4}{3}$

Step 4

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

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

$x + 1 = \frac{4}{3}$

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

Subtract $1$ from both sides of the equation.

$x = \frac{4}{3} - 1$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = \frac{4}{3} - 1 \cdot \frac{3}{3}$

Combine $- 1$ and $\frac{3}{3}$ .

$x = \frac{4}{3} + \frac{- 1 \cdot 3}{3}$

Combine the numerators over the common denominator.

$x = \frac{4 - 1 \cdot 3}{3}$

Simplify the numerator.

Multiply $- 1$ by $3$ .

$x = \frac{4 - 3}{3}$

Subtract $3$ from $4$ .

$x = \frac{1}{3}$

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

$x + 1 = - \frac{4}{3}$

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

Subtract $1$ from both sides of the equation.

$x = - \frac{4}{3} - 1$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x = - \frac{4}{3} - 1 \cdot \frac{3}{3}$

Combine $- 1$ and $\frac{3}{3}$ .

$x = - \frac{4}{3} + \frac{- 1 \cdot 3}{3}$

Combine the numerators over the common denominator.

$x = \frac{- 4 - 1 \cdot 3}{3}$

Simplify the numerator.

Multiply $- 1$ by $3$ .

$x = \frac{- 4 - 3}{3}$

Subtract $3$ from $- 4$ .

$x = \frac{- 7}{3}$

Move the negative in front of the fraction.

$x = - \frac{7}{3}$

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

$x = \frac{1}{3}, - \frac{7}{3}$

Solve Using the Square Root Property 9(x+1)^2=16

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