Solve 5x^2-500=0

$$5 x ^ { 2 } - 500 = 0$$

Solve for x

$$x=10$$

$$x=-10$$

Steps Using Difference of Squares

Divide both sides by 5.

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

Consider x^{2}-100. Rewrite x^{2}-100 as x^{2}-10^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-10\right)\left(x+10\right)=0$$

To find equation solutions, solve x-10=0 and x+10=0.

$$x=10 x=-10$$

Steps by Finding Square Root

Add 500 to both sides. Anything plus zero gives itself.

$$5x^{2}=500$$

Divide both sides by 5.

$$x^{2}=\frac{500}{5}$$

Divide 500 by 5 to get 100.

$$x^{2}=100$$

Take the square root of both sides of the equation.

$$x=10 x=-10$$

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.

$$5x^{2}-500=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -500 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-500\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-500\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-500\right)}}{2\times 5}$$

Multiply -20 times -500.

$$x=\frac{0±\sqrt{10000}}{2\times 5}$$

Take the square root of 10000.

$$x=\frac{0±100}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±100}{10}$$

Now solve the equation x=\frac{0±100}{10} when ± is plus. Divide 100 by 10.

$$x=10$$

Now solve the equation x=\frac{0±100}{10} when ± is minus. Divide -100 by 10.

$$x=-10$$

The equation is now solved.

$$x=10 x=-10$$