Solve -5x^2-4=3

$$- 5 x ^ { 2 } - 4 = 3$$

Solve for x (complex solution)

$$x=-\frac{\sqrt{35}i}{5}\approx -0-1.183215957i$$

$$x=\frac{\sqrt{35}i}{5}\approx 1.183215957i$$

Steps by Finding Square Root

Add 4 to both sides.

$$-5x^{2}=3+4$$

Add 3 and 4 to get 7.

$$-5x^{2}=7$$

Divide both sides by -5.

$$x^{2}=-\frac{7}{5}$$

The equation is now solved.

$$x=\frac{\sqrt{35}i}{5} x=-\frac{\sqrt{35}i}{5}$$

Steps Using the Quadratic Formula

Subtract 3 from both sides.

$$-5x^{2}-4-3=0$$

Subtract 3 from -4 to get -7.

$$-5x^{2}-7=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -5 for a, 0 for b, and -7 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5\right)\left(-7\right)}}{2\left(-5\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-5\right)\left(-7\right)}}{2\left(-5\right)}$$

Multiply -4 times -5.

$$x=\frac{0±\sqrt{20\left(-7\right)}}{2\left(-5\right)}$$

Multiply 20 times -7.

$$x=\frac{0±\sqrt{-140}}{2\left(-5\right)}$$

Take the square root of -140.

$$x=\frac{0±2\sqrt{35}i}{2\left(-5\right)}$$

Multiply 2 times -5.

$$x=\frac{0±2\sqrt{35}i}{-10}$$

Now solve the equation x=\frac{0±2\sqrt{35}i}{-10} when ± is plus.

$$x=-\frac{\sqrt{35}i}{5}$$

Now solve the equation x=\frac{0±2\sqrt{35}i}{-10} when ± is minus.

$$x=\frac{\sqrt{35}i}{5}$$

The equation is now solved.

$$x=-\frac{\sqrt{35}i}{5} x=\frac{\sqrt{35}i}{5}$$