Solve 6y^2+25=0

$$6 y ^ { 2 } + 25 = 0$$

Solve for y

$$y=-\frac{5\sqrt{6}i}{6}\approx -0-2.041241452i$$

$$y=\frac{5\sqrt{6}i}{6}\approx 2.041241452i$$

Steps by Finding Square Root

Subtract 25 from both sides. Anything subtracted from zero gives its negation.

$$6y^{2}=-25$$

Divide both sides by 6.

$$y^{2}=-\frac{25}{6}$$

The equation is now solved.

$$y=\frac{5\sqrt{6}i}{6} y=-\frac{5\sqrt{6}i}{6}$$

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.

$$6y^{2}+25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 6 for a, 0 for b, and 25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{0±\sqrt{0^{2}-4\times 6\times 25}}{2\times 6}$$

Square 0.

$$y=\frac{0±\sqrt{-4\times 6\times 25}}{2\times 6}$$

Multiply -4 times 6.

$$y=\frac{0±\sqrt{-24\times 25}}{2\times 6}$$

Multiply -24 times 25.

$$y=\frac{0±\sqrt{-600}}{2\times 6}$$

Take the square root of -600.

$$y=\frac{0±10\sqrt{6}i}{2\times 6}$$

Multiply 2 times 6.

$$y=\frac{0±10\sqrt{6}i}{12}$$

Now solve the equation y=\frac{0±10\sqrt{6}i}{12} when ± is plus.

$$y=\frac{5\sqrt{6}i}{6}$$

Now solve the equation y=\frac{0±10\sqrt{6}i}{12} when ± is minus.

$$y=-\frac{5\sqrt{6}i}{6}$$

The equation is now solved.

$$y=\frac{5\sqrt{6}i}{6} y=-\frac{5\sqrt{6}i}{6}$$