Solve Using the Square Root Property x^2-8x=242

$x^{2} - 8 x = 242$

Step 1

Subtract $242$ from both sides of the equation.

$x^{2} - 8 x - 242 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = - 8$ , and $c = - 242$ into the quadratic formula and solve for $x$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (1 \cdot - 242)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot - 242}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 242$ .

Multiply $- 4$ by $1$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot - 242}}{2 \cdot 1}$

Multiply $- 4$ by $- 242$ .

$x = \frac{8 \pm \sqrt{64 + 968}}{2 \cdot 1}$

Add $64$ and $968$ .

$x = \frac{8 \pm \sqrt{1032}}{2 \cdot 1}$

Rewrite $1032$ as $2^{2} \cdot 258$ .

Factor $4$ out of $1032$ .

$x = \frac{8 \pm \sqrt{4 (258)}}{2 \cdot 1}$

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

$x = \frac{8 \pm \sqrt{2^{2} \cdot 258}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{8 \pm 2 \sqrt{258}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{8 \pm 2 \sqrt{258}}{2}$

Simplify $\frac{8 \pm 2 \sqrt{258}}{2}$ .

$x = 4 \pm \sqrt{258}$

Step 5

Simplify the expression to solve for the $+$ portion of the $\pm$ .

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot - 242}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 242$ .

Multiply $- 4$ by $1$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot - 242}}{2 \cdot 1}$

Multiply $- 4$ by $- 242$ .

$x = \frac{8 \pm \sqrt{64 + 968}}{2 \cdot 1}$

Add $64$ and $968$ .

$x = \frac{8 \pm \sqrt{1032}}{2 \cdot 1}$

Rewrite $1032$ as $2^{2} \cdot 258$ .

Factor $4$ out of $1032$ .

$x = \frac{8 \pm \sqrt{4 (258)}}{2 \cdot 1}$

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

$x = \frac{8 \pm \sqrt{2^{2} \cdot 258}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{8 \pm 2 \sqrt{258}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{8 \pm 2 \sqrt{258}}{2}$

Simplify $\frac{8 \pm 2 \sqrt{258}}{2}$ .

$x = 4 \pm \sqrt{258}$

Change the $\pm$ to $+$ .

$x = 4 + \sqrt{258}$

Step 6

Simplify the expression to solve for the $-$ portion of the $\pm$ .

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot - 242}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 242$ .

Multiply $- 4$ by $1$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot - 242}}{2 \cdot 1}$

Multiply $- 4$ by $- 242$ .

$x = \frac{8 \pm \sqrt{64 + 968}}{2 \cdot 1}$

Add $64$ and $968$ .

$x = \frac{8 \pm \sqrt{1032}}{2 \cdot 1}$

Rewrite $1032$ as $2^{2} \cdot 258$ .

Factor $4$ out of $1032$ .

$x = \frac{8 \pm \sqrt{4 (258)}}{2 \cdot 1}$

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

$x = \frac{8 \pm \sqrt{2^{2} \cdot 258}}{2 \cdot 1}$

Pull terms out from under the radical.

$x = \frac{8 \pm 2 \sqrt{258}}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{8 \pm 2 \sqrt{258}}{2}$

Simplify $\frac{8 \pm 2 \sqrt{258}}{2}$ .

$x = 4 \pm \sqrt{258}$

Change the $\pm$ to $-$ .

$x = 4 - \sqrt{258}$

Step 7

The final answer is the combination of both solutions.

$x = 4 + \sqrt{258}, 4 - \sqrt{258}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = 4 + \sqrt{258}, 4 - \sqrt{258}$

Decimal Form:

$x = 20.06237840 \dots, - 12.06237840 \dots$

Solve Using the Square Root Property x^2-8x=242

Related Questions

Support LCMGCF.com by disabling your adblocker.