Solve r^2-100=0

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

Solve for r

$$r=10$$

$$r=-10$$

Steps Using Difference of Squares

Consider r^{2}-100. Rewrite r^{2}-100 as r^{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).

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

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

$$r=10 r=-10$$

Steps by Finding Square Root

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

$$r^{2}=100$$

Take the square root of both sides of the equation.

$$r=10 r=-10$$

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.

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

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -100 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 0.

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

Multiply -4 times -100.

$$r=\frac{0±\sqrt{400}}{2}$$

Take the square root of 400.

$$r=\frac{0±20}{2}$$

Now solve the equation r=\frac{0±20}{2} when ± is plus. Divide 20 by 2.

$$r=10$$

Now solve the equation r=\frac{0±20}{2} when ± is minus. Divide -20 by 2.

$$r=-10$$

The equation is now solved.

$$r=10 r=-10$$