Solve x^2+1=1/0.682

$${ x }^{ 2 } +1= \frac{ 1 }{ 0.682 }$$

Solve for x

$$x=\frac{\sqrt{54219}}{341}\approx 0.682843803$$

$$x=-\frac{\sqrt{54219}}{341}\approx -0.682843803$$

Steps by Finding Square Root

Expand \frac{1}{0.682} by multiplying both numerator and the denominator by 1000.

$$x^{2}+1=\frac{1000}{682}$$

Reduce the fraction \frac{1000}{682} to lowest terms by extracting and canceling out 2.

$$x^{2}+1=\frac{500}{341}$$

Subtract 1 from both sides.

$$x^{2}=\frac{500}{341}-1$$

Subtract 1 from \frac{500}{341} to get \frac{159}{341}.

$$x^{2}=\frac{159}{341}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{54219}}{341} x=-\frac{\sqrt{54219}}{341}$$

Steps Using the Quadratic Formula

Expand \frac{1}{0.682} by multiplying both numerator and the denominator by 1000.

$$x^{2}+1=\frac{1000}{682}$$

Reduce the fraction \frac{1000}{682} to lowest terms by extracting and canceling out 2.

$$x^{2}+1=\frac{500}{341}$$

Subtract \frac{500}{341} from both sides.

$$x^{2}+1-\frac{500}{341}=0$$

Subtract \frac{500}{341} from 1 to get -\frac{159}{341}.

$$x^{2}-\frac{159}{341}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{159}{341} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{159}{341}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{159}{341}\right)}}{2}$$

Multiply -4 times -\frac{159}{341}.

$$x=\frac{0±\sqrt{\frac{636}{341}}}{2}$$

Take the square root of \frac{636}{341}.

$$x=\frac{0±\frac{2\sqrt{54219}}{341}}{2}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{54219}}{341}}{2} when ± is plus.

$$x=\frac{\sqrt{54219}}{341}$$

Now solve the equation x=\frac{0±\frac{2\sqrt{54219}}{341}}{2} when ± is minus.

$$x=-\frac{\sqrt{54219}}{341}$$

The equation is now solved.

$$x=\frac{\sqrt{54219}}{341} x=-\frac{\sqrt{54219}}{341}$$