Solve x^2+1/5=17

$$x ^ { 2 } + \frac { 1 } { 5 } = 17$$

Solve for x

$$x = \frac{2 \sqrt{105}}{5} \approx 4.098780306$$

$$x = -\frac{2 \sqrt{105}}{5} \approx -4.098780306$$

Steps by Finding Square Root

Subtract \frac{1}{5} from both sides.

$$x^{2}=17-\frac{1}{5}$$

Subtract \frac{1}{5} from 17 to get \frac{84}{5}.

$$x^{2}=\frac{84}{5}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{105}}{5} x=-\frac{2\sqrt{105}}{5}$$

Steps Using the Quadratic Formula

Subtract 17 from both sides.

$$x^{2}+\frac{1}{5}-17=0$$

Subtract 17 from \frac{1}{5} to get -\frac{84}{5}.

$$x^{2}-\frac{84}{5}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{84}{5} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{84}{5}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{84}{5}\right)}}{2}$$

Multiply -4 times -\frac{84}{5}.

$$x=\frac{0±\sqrt{\frac{336}{5}}}{2}$$

Take the square root of \frac{336}{5}.

$$x=\frac{0±\frac{4\sqrt{105}}{5}}{2}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{105}}{5}}{2} when ± is plus.

$$x=\frac{2\sqrt{105}}{5}$$

Now solve the equation x=\frac{0±\frac{4\sqrt{105}}{5}}{2} when ± is minus.

$$x=-\frac{2\sqrt{105}}{5}$$

The equation is now solved.

$$x=\frac{2\sqrt{105}}{5} x=-\frac{2\sqrt{105}}{5}$$