Solve 6x^2+25=0

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

Solve for x (complex solution)

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

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

Steps by Finding Square Root

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

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

Divide both sides by 6.

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

The equation is now solved.

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

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.

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

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}.

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

Square 0.

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

Multiply -4 times 6.

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

Multiply -24 times 25.

$$x=\frac{0±\sqrt{-600}}{2\times 6}$$

Take the square root of -600.

$$x=\frac{0±10\sqrt{6}i}{2\times 6}$$

Multiply 2 times 6.

$$x=\frac{0±10\sqrt{6}i}{12}$$

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

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

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

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

The equation is now solved.

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