Solve x^2-1/4-15/32=0

$${ x }^{ 2 } - \frac{ 1 }{ 4 } - \frac{ 15 }{ 32 } =0$$

Solve for x

$$x=\frac{\sqrt{46}}{8}\approx 0.847791248$$

$$x=-\frac{\sqrt{46}}{8}\approx -0.847791248$$

Steps by Finding Square Root

Subtract \frac{15}{32} from -\frac{1}{4} to get -\frac{23}{32}.

$$x^{2}-\frac{23}{32}=0$$

Add \frac{23}{32} to both sides. Anything plus zero gives itself.

$$x^{2}=\frac{23}{32}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{46}}{8} x=-\frac{\sqrt{46}}{8}$$

Steps Using the Quadratic Formula

Subtract \frac{15}{32} from -\frac{1}{4} to get -\frac{23}{32}.

$$x^{2}-\frac{23}{32}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{23}{32} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{23}{32}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{23}{32}\right)}}{2}$$

Multiply -4 times -\frac{23}{32}.

$$x=\frac{0±\sqrt{\frac{23}{8}}}{2}$$

Take the square root of \frac{23}{8}.

$$x=\frac{0±\frac{\sqrt{46}}{4}}{2}$$

Now solve the equation x=\frac{0±\frac{\sqrt{46}}{4}}{2} when ± is plus.

$$x=\frac{\sqrt{46}}{8}$$

Now solve the equation x=\frac{0±\frac{\sqrt{46}}{4}}{2} when ± is minus.

$$x=-\frac{\sqrt{46}}{8}$$

The equation is now solved.

$$x=\frac{\sqrt{46}}{8} x=-\frac{\sqrt{46}}{8}$$