Solve -5x^2+45=0

$$-5 { x }^{ 2 } +45=0$$

Solve for x

$$x=3$$

$$x=-3$$

Steps by Finding Square Root

Subtract 45 from both sides. Anything subtracted from zero gives its negation.

$$-5x^{2}=-45$$

Divide both sides by -5.

$$x^{2}=\frac{-45}{-5}$$

Divide -45 by -5 to get 9.

$$x^{2}=9$$

Take the square root of both sides of the equation.

$$x=3 x=-3$$

Steps Using the Quadratic Formula

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-5x^{2}+45=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -5 for a, 0 for b, and 45 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5\right)\times 45}}{2\left(-5\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-5\right)\times 45}}{2\left(-5\right)}$$

Multiply -4 times -5.

$$x=\frac{0±\sqrt{20\times 45}}{2\left(-5\right)}$$

Multiply 20 times 45.

$$x=\frac{0±\sqrt{900}}{2\left(-5\right)}$$

Take the square root of 900.

$$x=\frac{0±30}{2\left(-5\right)}$$

Multiply 2 times -5.

$$x=\frac{0±30}{-10}$$

Now solve the equation x=\frac{0±30}{-10} when ± is plus. Divide 30 by -10.

$$x=-3$$

Now solve the equation x=\frac{0±30}{-10} when ± is minus. Divide -30 by -10.

$$x=3$$

The equation is now solved.

$$x=-3 x=3$$