Solve 25x^2+4=0

$$25 x ^ { 2 } + 4 = 0$$

Solve for x (complex solution)

$$x=-\frac{2}{5}i=-0.4i$$

$$x=\frac{2}{5}i=0.4i$$

Steps by Finding Square Root

Subtract 4 from both sides. Anything subtracted from zero gives its negation.

$$25x^{2}=-4$$

Divide both sides by 25.

$$x^{2}=-\frac{4}{25}$$

The equation is now solved.

$$x=\frac{2}{5}i x=-\frac{2}{5}i$$

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.

$$25x^{2}+4=0$$

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

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

Square 0.

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

Multiply -4 times 25.

$$x=\frac{0±\sqrt{-100\times 4}}{2\times 25}$$

Multiply -100 times 4.

$$x=\frac{0±\sqrt{-400}}{2\times 25}$$

Take the square root of -400.

$$x=\frac{0±20i}{2\times 25}$$

Multiply 2 times 25.

$$x=\frac{0±20i}{50}$$

Now solve the equation x=\frac{0±20i}{50} when ± is plus.

$$x=\frac{2}{5}i$$

Now solve the equation x=\frac{0±20i}{50} when ± is minus.

$$x=-\frac{2}{5}i$$

The equation is now solved.

$$x=\frac{2}{5}i x=-\frac{2}{5}i$$