Solve 4x^2+75=0

$$4 x ^ { 2 } + 75 = 0$$

Solve for x (complex solution)

$$x=-\frac{5\sqrt{3}i}{2}\approx -0-4.330127019i$$

$$x=\frac{5\sqrt{3}i}{2}\approx 4.330127019i$$

Steps by Finding Square Root

Subtract 75 from both sides. Anything subtracted from zero gives its negation.

$$4x^{2}=-75$$

Divide both sides by 4.

$$x^{2}=-\frac{75}{4}$$

The equation is now solved.

$$x=\frac{5\sqrt{3}i}{2} x=-\frac{5\sqrt{3}i}{2}$$

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.

$$4x^{2}+75=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and 75 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\times 75}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\times 75}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\times 75}}{2\times 4}$$

Multiply -16 times 75.

$$x=\frac{0±\sqrt{-1200}}{2\times 4}$$

Take the square root of -1200.

$$x=\frac{0±20\sqrt{3}i}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±20\sqrt{3}i}{8}$$

Now solve the equation x=\frac{0±20\sqrt{3}i}{8} when ± is plus.

$$x=\frac{5\sqrt{3}i}{2}$$

Now solve the equation x=\frac{0±20\sqrt{3}i}{8} when ± is minus.

$$x=-\frac{5\sqrt{3}i}{2}$$

The equation is now solved.

$$x=\frac{5\sqrt{3}i}{2} x=-\frac{5\sqrt{3}i}{2}$$