Solve 5x^2-125=0

$$5 { x }^{ 2 } -125=0$$

Solve for x

$$x=5$$

$$x=-5$$

Steps Using Difference of Squares

Divide both sides by 5.

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

Consider x^{2}-25. Rewrite x^{2}-25 as x^{2}-5^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-5\right)\left(x+5\right)=0$$

To find equation solutions, solve x-5=0 and x+5=0.

$$x=5 x=-5$$

Steps by Finding Square Root

Add 125 to both sides. Anything plus zero gives itself.

$$5x^{2}=125$$

Divide both sides by 5.

$$x^{2}=\frac{125}{5}$$

Divide 125 by 5 to get 25.

$$x^{2}=25$$

Take the square root of both sides of the equation.

$$x=5 x=-5$$

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.

$$5x^{2}-125=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -125 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 5\left(-125\right)}}{2\times 5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 5\left(-125\right)}}{2\times 5}$$

Multiply -4 times 5.

$$x=\frac{0±\sqrt{-20\left(-125\right)}}{2\times 5}$$

Multiply -20 times -125.

$$x=\frac{0±\sqrt{2500}}{2\times 5}$$

Take the square root of 2500.

$$x=\frac{0±50}{2\times 5}$$

Multiply 2 times 5.

$$x=\frac{0±50}{10}$$

Now solve the equation x=\frac{0±50}{10} when ± is plus. Divide 50 by 10.

$$x=5$$

Now solve the equation x=\frac{0±50}{10} when ± is minus. Divide -50 by 10.

$$x=-5$$

The equation is now solved.

$$x=5 x=-5$$