Solve 1=-4x^2-3

$$1=-4 { x }^{ 2 } -3$$

Solve for x (complex solution)

$$x=-i$$

$$x=i$$

Steps by Finding Square Root

Swap sides so that all variable terms are on the left hand side.

$$-4x^{2}-3=1$$

Add 3 to both sides.

$$-4x^{2}=1+3$$

Add 1 and 3 to get 4.

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

Divide both sides by -4.

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

Divide 4 by -4 to get -1.

$$x^{2}=-1$$

The equation is now solved.

$$x=i x=-i$$

Steps Using the Quadratic Formula

Swap sides so that all variable terms are on the left hand side.

$$-4x^{2}-3=1$$

Subtract 1 from both sides.

$$-4x^{2}-3-1=0$$

Subtract 1 from -3 to get -4.

$$-4x^{2}-4=0$$

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

$$x=\frac{0±\sqrt{0^{2}-4\left(-4\right)\left(-4\right)}}{2\left(-4\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-4\right)\left(-4\right)}}{2\left(-4\right)}$$

Multiply -4 times -4.

$$x=\frac{0±\sqrt{16\left(-4\right)}}{2\left(-4\right)}$$

Multiply 16 times -4.

$$x=\frac{0±\sqrt{-64}}{2\left(-4\right)}$$

Take the square root of -64.

$$x=\frac{0±8i}{2\left(-4\right)}$$

Multiply 2 times -4.

$$x=\frac{0±8i}{-8}$$

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

$$x=-i$$

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

$$x=i$$

The equation is now solved.

$$x=-i x=i$$