Solve 5x^2-100=0

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

Solve for x

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

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

Steps by Finding Square Root

Add 100 to both sides. Anything plus zero gives itself.

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

Divide both sides by 5.

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

Divide 100 by 5 to get 20.

$$x^{2}=20$$

Take the square root of both sides of the equation.

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

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.

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

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}.

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

Square 0.

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

Multiply -4 times 5.

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

Multiply -20 times -100.

$$x=\frac{0±\sqrt{2000}}{2\times 5}$$

Take the square root of 2000.

$$x=\frac{0±20\sqrt{5}}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±20\sqrt{5}}{10}$$

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

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

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

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

The equation is now solved.

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