Solve Using the Square Root Property (11x+7)^2=105

${(11 x + 7)}^{2} = 105$

Step 1

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

$11 x + 7 = \pm \sqrt{105}$

Step 2

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.

$11 x + 7 = \sqrt{105}$

Subtract $7$ from both sides of the equation.

$11 x = \sqrt{105} - 7$

Divide each term in $11 x = \sqrt{105} - 7$ by $11$ and simplify.

Divide each term in $11 x = \sqrt{105} - 7$ by $11$ .

$\frac{11 x}{11} = \frac{\sqrt{105}}{11} + \frac{- 7}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} = \frac{\sqrt{105}}{11} + \frac{- 7}{11}$

Divide $x$ by $1$ .

$x = \frac{\sqrt{105}}{11} + \frac{- 7}{11}$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{\sqrt{105}}{11} - \frac{7}{11}$

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

$11 x + 7 = - \sqrt{105}$

Subtract $7$ from both sides of the equation.

$11 x = - \sqrt{105} - 7$

Divide each term in $11 x = - \sqrt{105} - 7$ by $11$ and simplify.

Divide each term in $11 x = - \sqrt{105} - 7$ by $11$ .

$\frac{11 x}{11} = \frac{- \sqrt{105}}{11} + \frac{- 7}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} = \frac{- \sqrt{105}}{11} + \frac{- 7}{11}$

Divide $x$ by $1$ .

$x = \frac{- \sqrt{105}}{11} + \frac{- 7}{11}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{\sqrt{105}}{11} + \frac{- 7}{11}$

Move the negative in front of the fraction.

$x = - \frac{\sqrt{105}}{11} - \frac{7}{11}$

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

$x = \frac{\sqrt{105}}{11} - \frac{7}{11}, - \frac{\sqrt{105}}{11} - \frac{7}{11}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{105}}{11} - \frac{7}{11}, - \frac{\sqrt{105}}{11} - \frac{7}{11}$

Decimal Form:

$x = 0.29517734 \dots, - 1.56790461 \dots$

Solve Using the Square Root Property (11x+7)^2=105

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