Solve 132(x^2-1)=x^2+7

$$132 ( x ^ { 2 } - 1 ) = x ^ { 2 } + 7$$

Solve for x

$$x = \frac{\sqrt{18209}}{131} \approx 1.030081891$$

$$x = -\frac{\sqrt{18209}}{131} \approx -1.030081891$$

Steps by Finding Square Root

Use the distributive property to multiply 132 by x^{2}-1.

$$132x^{2}-132=x^{2}+7$$

Subtract x^{2} from both sides.

$$132x^{2}-132-x^{2}=7$$

Combine 132x^{2} and -x^{2} to get 131x^{2}.

$$131x^{2}-132=7$$

Add 132 to both sides.

$$131x^{2}=7+132$$

Add 7 and 132 to get 139.

$$131x^{2}=139$$

Divide both sides by 131.

$$x^{2}=\frac{139}{131}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{18209}}{131} x=-\frac{\sqrt{18209}}{131}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 132 by x^{2}-1.

$$132x^{2}-132=x^{2}+7$$

Subtract x^{2} from both sides.

$$132x^{2}-132-x^{2}=7$$

Combine 132x^{2} and -x^{2} to get 131x^{2}.

$$131x^{2}-132=7$$

Subtract 7 from both sides.

$$131x^{2}-132-7=0$$

Subtract 7 from -132 to get -139.

$$131x^{2}-139=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 131 for a, 0 for b, and -139 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 131\left(-139\right)}}{2\times 131}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 131\left(-139\right)}}{2\times 131}$$

Multiply -4 times 131.

$$x=\frac{0±\sqrt{-524\left(-139\right)}}{2\times 131}$$

Multiply -524 times -139.

$$x=\frac{0±\sqrt{72836}}{2\times 131}$$

Take the square root of 72836.

$$x=\frac{0±2\sqrt{18209}}{2\times 131}$$

Multiply 2 times 131.

$$x=\frac{0±2\sqrt{18209}}{262}$$

Now solve the equation x=\frac{0±2\sqrt{18209}}{262} when ± is plus.

$$x=\frac{\sqrt{18209}}{131}$$

Now solve the equation x=\frac{0±2\sqrt{18209}}{262} when ± is minus.

$$x=-\frac{\sqrt{18209}}{131}$$

The equation is now solved.

$$x=\frac{\sqrt{18209}}{131} x=-\frac{\sqrt{18209}}{131}$$