Solve 5x^2+25=0

$$5 x ^ { 2 } + 25 = 0$$

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

$$5x^{2}=-25$$

Divide both sides by 5.

$$x^{2}=\frac{-25}{5}$$

Divide -25 by 5 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.

$$5x^{2}+25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and 25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\times 25}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\times 25}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\times 25}}{2\times 5}$$

Multiply -20 times 25.

$$x=\frac{0±\sqrt{-500}}{2\times 5}$$

Take the square root of -500.

$$x=\frac{0±10\sqrt{5}i}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±10\sqrt{5}i}{10}$$

Now solve the equation x=\frac{0±10\sqrt{5}i}{10} when ± is plus.

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

Now solve the equation x=\frac{0±10\sqrt{5}i}{10} when ± is minus.

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

The equation is now solved.

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