Solve x^2+1/25=1

$$x ^ { 2 } + \frac { 1 } { 25 } = 1$$

Solve for x

$$x=\frac{2\sqrt{6}}{5}\approx 0.979795897$$

$$x=-\frac{2\sqrt{6}}{5}\approx -0.979795897$$

Steps by Finding Square Root

Subtract \frac{1}{25} from both sides.

$$x^{2}=1-\frac{1}{25}$$

Subtract \frac{1}{25} from 1 to get \frac{24}{25}.

$$x^{2}=\frac{24}{25}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{6}}{5} x=-\frac{2\sqrt{6}}{5}$$

Steps Using the Quadratic Formula

Subtract 1 from both sides.

$$x^{2}+\frac{1}{25}-1=0$$

Subtract 1 from \frac{1}{25} to get -\frac{24}{25}.

$$x^{2}-\frac{24}{25}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{24}{25} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{24}{25}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{24}{25}\right)}}{2}$$

Multiply -4 times -\frac{24}{25}.

$$x=\frac{0±\sqrt{\frac{96}{25}}}{2}$$

Take the square root of \frac{96}{25}.

$$x=\frac{0±\frac{4\sqrt{6}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{6}}{5}}{2} when ± is plus.

$$x=\frac{2\sqrt{6}}{5}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{6}}{5}}{2} when ± is minus.

$$x=-\frac{2\sqrt{6}}{5}$$

The equation is now solved.

$$x=\frac{2\sqrt{6}}{5} x=-\frac{2\sqrt{6}}{5}$$