Solve 4x^2+29=10

$$4 x ^ { 2 } + 29 = 10$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{19}i}{2}\approx -0-2.179449472i$$

$$x=\frac{\sqrt{19}i}{2}\approx 2.179449472i$$

Steps by Finding Square Root

Subtract 29 from both sides.

$$4x^{2}=10-29$$

Subtract 29 from 10 to get -19.

$$4x^{2}=-19$$

Divide both sides by 4.

$$x^{2}=-\frac{19}{4}$$

The equation is now solved.

$$x=\frac{\sqrt{19}i}{2} x=-\frac{\sqrt{19}i}{2}$$

Steps Using the Quadratic Formula

Subtract 10 from both sides.

$$4x^{2}+29-10=0$$

Subtract 10 from 29 to get 19.

$$4x^{2}+19=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and 19 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\times 19}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\times 19}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\times 19}}{2\times 4}$$

Multiply -16 times 19.

$$x=\frac{0±\sqrt{-304}}{2\times 4}$$

Take the square root of -304.

$$x=\frac{0±4\sqrt{19}i}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±4\sqrt{19}i}{8}$$

Now solve the equation x=\frac{0±4\sqrt{19}i}{8} when ± is plus.

$$x=\frac{\sqrt{19}i}{2}$$

Now solve the equation x=\frac{0±4\sqrt{19}i}{8} when ± is minus.

$$x=-\frac{\sqrt{19}i}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{19}i}{2} x=-\frac{\sqrt{19}i}{2}$$