Solve y^2-15=-54

$${ y }^{ 2 } -15=-54$$

Solve for y

$$y=-\sqrt{39}i\approx -0-6.244997998i$$

$$y=\sqrt{39}i\approx 6.244997998i$$

Steps by Finding Square Root

Add 15 to both sides.

$$y^{2}=-54+15$$

Add -54 and 15 to get -39.

$$y^{2}=-39$$

The equation is now solved.

$$y=\sqrt{39}i y=-\sqrt{39}i$$

Steps Using the Quadratic Formula

Add 54 to both sides.

$$y^{2}-15+54=0$$

Add -15 and 54 to get 39.

$$y^{2}+39=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and 39 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 39}}{2}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 39}}{2}$$

Multiply -4 times 39.

$$y=\frac{0±\sqrt{-156}}{2}$$

Take the square root of -156.

$$y=\frac{0±2\sqrt{39}i}{2}$$

Now solve the equation y=\frac{0±2\sqrt{39}i}{2} when ± is plus.

$$y=\sqrt{39}i$$

Now solve the equation y=\frac{0±2\sqrt{39}i}{2} when ± is minus.

$$y=-\sqrt{39}i$$

The equation is now solved.

$$y=\sqrt{39}i y=-\sqrt{39}i$$