Solve 5x^2+40=-60

$$5 x ^ { 2 } + 40 = - 60$$

Solve for x (complex solution)

$$x=-2\sqrt{5}i\approx -0-4.472135955i$$

$$x=2\sqrt{5}i\approx 4.472135955i$$

Steps by Finding Square Root

Subtract 40 from both sides.

$$5x^{2}=-60-40$$

Subtract 40 from -60 to get -100.

$$5x^{2}=-100$$

Divide both sides by 5.

$$x^{2}=\frac{-100}{5}$$

Divide -100 by 5 to get -20.

$$x^{2}=-20$$

The equation is now solved.

$$x=2\sqrt{5}i x=-2\sqrt{5}i$$

Steps Using the Quadratic Formula

Add 60 to both sides.

$$5x^{2}+40+60=0$$

Add 40 and 60 to get 100.

$$5x^{2}+100=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and 100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\times 100}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\times 100}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\times 100}}{2\times 5}$$

Multiply -20 times 100.

$$x=\frac{0±\sqrt{-2000}}{2\times 5}$$

Take the square root of -2000.

$$x=\frac{0±20\sqrt{5}i}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±20\sqrt{5}i}{10}$$

Now solve the equation x=\frac{0±20\sqrt{5}i}{10} when ± is plus.

$$x=2\sqrt{5}i$$

Now solve the equation x=\frac{0±20\sqrt{5}i}{10} when ± is minus.

$$x=-2\sqrt{5}i$$

The equation is now solved.

$$x=2\sqrt{5}i x=-2\sqrt{5}i$$