Solve 4x^2+25=5

$$4 x ^ { 2 } + 25 = 5$$

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.

$$4x^{2}=5-25$$

Subtract 25 from 5 to get -20.

$$4x^{2}=-20$$

Divide both sides by 4.

$$x^{2}=\frac{-20}{4}$$

Divide -20 by 4 to get -5.

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

The equation is now solved.

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

Steps Using the Quadratic Formula

Subtract 5 from both sides.

$$4x^{2}+25-5=0$$

Subtract 5 from 25 to get 20.

$$4x^{2}+20=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and 20 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\times 20}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\times 20}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\times 20}}{2\times 4}$$

Multiply -16 times 20.

$$x=\frac{0±\sqrt{-320}}{2\times 4}$$

Take the square root of -320.

$$x=\frac{0±8\sqrt{5}i}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±8\sqrt{5}i}{8}$$

Now solve the equation x=\frac{0±8\sqrt{5}i}{8} when ± is plus.

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

Now solve the equation x=\frac{0±8\sqrt{5}i}{8} when ± is minus.

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

The equation is now solved.

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