Solve 4x^2+64=-17

$$4 x ^ { 2 } + 64 = - 17$$

Solve for x (complex solution)

$$x=-\frac{9}{2}i=-4.5i$$

$$x=\frac{9}{2}i=4.5i$$

Steps by Finding Square Root

Subtract 64 from both sides.

$$4x^{2}=-17-64$$

Subtract 64 from -17 to get -81.

$$4x^{2}=-81$$

Divide both sides by 4.

$$x^{2}=-\frac{81}{4}$$

The equation is now solved.

$$x=\frac{9}{2}i x=-\frac{9}{2}i$$

Steps Using the Quadratic Formula

Add 17 to both sides.

$$4x^{2}+64+17=0$$

Add 64 and 17 to get 81.

$$4x^{2}+81=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and 81 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\times 81}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\times 81}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\times 81}}{2\times 4}$$

Multiply -16 times 81.

$$x=\frac{0±\sqrt{-1296}}{2\times 4}$$

Take the square root of -1296.

$$x=\frac{0±36i}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±36i}{8}$$

Now solve the equation x=\frac{0±36i}{8} when ± is plus.

$$x=\frac{9}{2}i$$

Now solve the equation x=\frac{0±36i}{8} when ± is minus.

$$x=-\frac{9}{2}i$$

The equation is now solved.

$$x=\frac{9}{2}i x=-\frac{9}{2}i$$