Solve 25x^2+125=0

$$25 { x }^{ 2 } +125=0$$

Solve for x (complex solution)

$$x=-\sqrt{5}i\approx -0-2.236067977i$$

$$x=\sqrt{5}i\approx 2.236067977i$$

Steps by Finding Square Root

Subtract 125 from both sides. Anything subtracted from zero gives its negation.

$$25x^{2}=-125$$

Divide both sides by 25.

$$x^{2}=\frac{-125}{25}$$

Divide -125 by 25 to get -5.

$$x^{2}=-5$$

The equation is now solved.

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

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.

$$25x^{2}+125=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 25 for a, 0 for b, and 125 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 25\times 125}}{2\times 25}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 25\times 125}}{2\times 25}$$

Multiply -4 times 25.

$$x=\frac{0±\sqrt{-100\times 125}}{2\times 25}$$

Multiply -100 times 125.

$$x=\frac{0±\sqrt{-12500}}{2\times 25}$$

Take the square root of -12500.

$$x=\frac{0±50\sqrt{5}i}{2\times 25}$$

Multiply 2 times 25.

$$x=\frac{0±50\sqrt{5}i}{50}$$

Now solve the equation x=\frac{0±50\sqrt{5}i}{50} when ± is plus.

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

Now solve the equation x=\frac{0±50\sqrt{5}i}{50} when ± is minus.

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

The equation is now solved.

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