Solve z^2-3/2+9/16=0

$$z ^ { 2 } - \frac { 3 } { 2 } + \frac { 9 } { 16 } = 0$$

Solve for z

$$z=\frac{\sqrt{15}}{4}\approx 0.968245837$$

$$z=-\frac{\sqrt{15}}{4}\approx -0.968245837$$

Steps by Finding Square Root

Add -\frac{3}{2} and \frac{9}{16} to get -\frac{15}{16}.

$$z^{2}-\frac{15}{16}=0$$

Add \frac{15}{16} to both sides. Anything plus zero gives itself.

$$z^{2}=\frac{15}{16}$$

Take the square root of both sides of the equation.

$$z=\frac{\sqrt{15}}{4} z=-\frac{\sqrt{15}}{4}$$

Steps Using the Quadratic Formula

Add -\frac{3}{2} and \frac{9}{16} to get -\frac{15}{16}.

$$z^{2}-\frac{15}{16}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{15}{16} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$z=\frac{0±\sqrt{0^{2}-4\left(-\frac{15}{16}\right)}}{2}$$

Square 0.

$$z=\frac{0±\sqrt{-4\left(-\frac{15}{16}\right)}}{2}$$

Multiply -4 times -\frac{15}{16}.

$$z=\frac{0±\sqrt{\frac{15}{4}}}{2}$$

Take the square root of \frac{15}{4}.

$$z=\frac{0±\frac{\sqrt{15}}{2}}{2}$$

Now solve the equation z=\frac{0±\frac{\sqrt{15}}{2}}{2} when ± is plus.

$$z=\frac{\sqrt{15}}{4}$$

Now solve the equation z=\frac{0±\frac{\sqrt{15}}{2}}{2} when ± is minus.

$$z=-\frac{\sqrt{15}}{4}$$

The equation is now solved.

$$z=\frac{\sqrt{15}}{4} z=-\frac{\sqrt{15}}{4}$$