Solve 25y^2+2=0

$$25 y ^ { 2 } + 2 = 0$$

Solve for y

$$y=-\frac{\sqrt{2}i}{5}\approx -0-0.282842712i$$

$$y=\frac{\sqrt{2}i}{5}\approx 0.282842712i$$

Steps by Finding Square Root

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$25y^{2}=-2$$

Divide both sides by 25.

$$y^{2}=-\frac{2}{25}$$

The equation is now solved.

$$y=\frac{\sqrt{2}i}{5} y=-\frac{\sqrt{2}i}{5}$$

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.

$$25y^{2}+2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 25 for a, 0 for b, and 2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 25\times 2}}{2\times 25}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 25\times 2}}{2\times 25}$$

Multiply -4 times 25.

$$y=\frac{0±\sqrt{-100\times 2}}{2\times 25}$$

Multiply -100 times 2.

$$y=\frac{0±\sqrt{-200}}{2\times 25}$$

Take the square root of -200.

$$y=\frac{0±10\sqrt{2}i}{2\times 25}$$

Multiply 2 times 25.

$$y=\frac{0±10\sqrt{2}i}{50}$$

Now solve the equation y=\frac{0±10\sqrt{2}i}{50} when ± is plus.

$$y=\frac{\sqrt{2}i}{5}$$

Now solve the equation y=\frac{0±10\sqrt{2}i}{50} when ± is minus.

$$y=-\frac{\sqrt{2}i}{5}$$

The equation is now solved.

$$y=\frac{\sqrt{2}i}{5} y=-\frac{\sqrt{2}i}{5}$$