Solve 5=10+20+-5x^2

$$5 = 10 + 20 + - 5 x ^ { 2 }$$

Solve for x

$$x=\sqrt{5}\approx 2.236067977$$

$$x=-\sqrt{5}\approx -2.236067977$$

Steps by Finding Square Root

Add 10 and 20 to get 30.

$$5=30-5x^{2}$$

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

$$30-5x^{2}=5$$

Subtract 30 from both sides.

$$-5x^{2}=5-30$$

Subtract 30 from 5 to get -25.

$$-5x^{2}=-25$$

Divide both sides by -5.

$$x^{2}=\frac{-25}{-5}$$

Divide -25 by -5 to get 5.

$$x^{2}=5$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

Add 10 and 20 to get 30.

$$5=30-5x^{2}$$

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

$$30-5x^{2}=5$$

Subtract 5 from both sides.

$$30-5x^{2}-5=0$$

Subtract 5 from 30 to get 25.

$$25-5x^{2}=0$$

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.

$$-5x^{2}+25=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -5 for a, 0 for b, and 25 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-5\right)\times 25}}{2\left(-5\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-5\right)\times 25}}{2\left(-5\right)}$$

Multiply -4 times -5.

$$x=\frac{0±\sqrt{20\times 25}}{2\left(-5\right)}$$

Multiply 20 times 25.

$$x=\frac{0±\sqrt{500}}{2\left(-5\right)}$$

Take the square root of 500.

$$x=\frac{0±10\sqrt{5}}{2\left(-5\right)}$$

Multiply 2 times -5.

$$x=\frac{0±10\sqrt{5}}{-10}$$

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

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

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

$$x=\sqrt{5}$$

The equation is now solved.

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