Solve Using the Square Root Property 10(x-7)^2=440

$10 {(x - 7)}^{2} = 440$

Step 1

Divide each term in $10 {(x - 7)}^{2} = 440$ by $10$ and simplify.

Divide each term in $10 {(x - 7)}^{2} = 440$ by $10$ .

$\frac{10 {(x - 7)}^{2}}{10} = \frac{440}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 {(x - 7)}^{2}}{10} = \frac{440}{10}$

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

${(x - 7)}^{2} = \frac{440}{10}$

Simplify the right side.

Divide $440$ by $10$ .

${(x - 7)}^{2} = 44$

Step 2

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

$x - 7 = \pm \sqrt{44}$

Step 3

Simplify $\pm \sqrt{44}$ .

Rewrite $44$ as $2^{2} \cdot 11$ .

Factor $4$ out of $44$ .

$x - 7 = \pm \sqrt{4 (11)}$

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

$x - 7 = \pm \sqrt{2^{2} \cdot 11}$

Pull terms out from under the radical.

$x - 7 = \pm 2 \sqrt{11}$

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.

$x - 7 = 2 \sqrt{11}$

Add $7$ to both sides of the equation.

$x = 2 \sqrt{11} + 7$

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

$x - 7 = - 2 \sqrt{11}$

Add $7$ to both sides of the equation.

$x = - 2 \sqrt{11} + 7$

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

$x = 2 \sqrt{11} + 7, - 2 \sqrt{11} + 7$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{11} + 7, - 2 \sqrt{11} + 7$

Decimal Form:

$x = 13.63324958 \dots, 0.36675041 \dots$