Solve 36y^2+40=0

$$36 { y }^{ 2 } +40 = 0$$

Solve for y

$$y=-\frac{\sqrt{10}i}{3}\approx -0-1.054092553i$$

$$y=\frac{\sqrt{10}i}{3}\approx 1.054092553i$$

Steps by Finding Square Root

Subtract 40 from both sides. Anything subtracted from zero gives its negation.

$$36y^{2}=-40$$

Divide both sides by 36.

$$y^{2}=\frac{-40}{36}$$

Reduce the fraction \frac{-40}{36} to lowest terms by extracting and canceling out 4.

$$y^{2}=-\frac{10}{9}$$

The equation is now solved.

$$y=\frac{\sqrt{10}i}{3} y=-\frac{\sqrt{10}i}{3}$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$36y^{2}+40=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 36 for a, 0 for b, and 40 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 36\times 40}}{2\times 36}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 36\times 40}}{2\times 36}$$

Multiply -4 times 36.

$$y=\frac{0±\sqrt{-144\times 40}}{2\times 36}$$

Multiply -144 times 40.

$$y=\frac{0±\sqrt{-5760}}{2\times 36}$$

Take the square root of -5760.

$$y=\frac{0±24\sqrt{10}i}{2\times 36}$$

Multiply 2 times 36.

$$y=\frac{0±24\sqrt{10}i}{72}$$

Now solve the equation y=\frac{0±24\sqrt{10}i}{72} when ± is plus.

$$y=\frac{\sqrt{10}i}{3}$$

Now solve the equation y=\frac{0±24\sqrt{10}i}{72} when ± is minus.

$$y=-\frac{\sqrt{10}i}{3}$$

The equation is now solved.

$$y=\frac{\sqrt{10}i}{3} y=-\frac{\sqrt{10}i}{3}$$