Solve (4x+3)^2+11=-17

$$( 4 x + 3 ) ^ { 2 } + 11 = - 17$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{7}i}{2}-\frac{3}{4}\approx -0.75-1.322875656i$$

$$x=\frac{\sqrt{7}i}{2}-\frac{3}{4}\approx -0.75+1.322875656i$$

Steps by Finding Square Root

Subtracting 11 from itself leaves 0.

$$\left(4x+3\right)^{2}=-17-11$$

Subtract 11 from -17.

$$\left(4x+3\right)^{2}=-28$$

Take the square root of both sides of the equation.

$$4x+3=2\sqrt{7}i 4x+3=-2\sqrt{7}i$$

Subtract 3 from both sides of the equation.

$$4x+3-3=2\sqrt{7}i-3 4x+3-3=-2\sqrt{7}i-3$$

Subtracting 3 from itself leaves 0.

$$4x=2\sqrt{7}i-3 4x=-2\sqrt{7}i-3$$

Subtract 3 from 2i\sqrt{7}.

$$4x=-3+2\sqrt{7}i$$

Subtract 3 from -2i\sqrt{7}.

$$4x=-2\sqrt{7}i-3$$

Divide both sides by 4.

$$\frac{4x}{4}=\frac{-3+2\sqrt{7}i}{4} \frac{4x}{4}=\frac{-2\sqrt{7}i-3}{4}$$

Dividing by 4 undoes the multiplication by 4.

$$x=\frac{-3+2\sqrt{7}i}{4} x=\frac{-2\sqrt{7}i-3}{4}$$

Divide 2i\sqrt{7}-3 by 4.

$$x=\frac{\sqrt{7}i}{2}-\frac{3}{4}$$

Divide -2i\sqrt{7}-3 by 4.

$$x=-\frac{\sqrt{7}i}{2}-\frac{3}{4}$$

The equation is now solved.

$$x=\frac{\sqrt{7}i}{2}-\frac{3}{4} x=-\frac{\sqrt{7}i}{2}-\frac{3}{4}$$