Solve r^2=(-83)^2

$$r ^ { 2 } = ( - 83 ) ^ { 2 }$$

Solve for r

$$r=83$$

$$r=-83$$

Steps Using Difference of Squares

Calculate -83 to the power of 2 and get 6889.

$$r^{2}=6889$$

Subtract 6889 from both sides.

$$r^{2}-6889=0$$

Consider r^{2}-6889. Rewrite r^{2}-6889 as r^{2}-83^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(r-83\right)\left(r+83\right)=0$$

To find equation solutions, solve r-83=0 and r+83=0.

$$r=83 r=-83$$

Steps by Finding Square Root

Calculate -83 to the power of 2 and get 6889.

$$r^{2}=6889$$

Take the square root of both sides of the equation.

$$r=83 r=-83$$

Steps Using the Quadratic Formula

Calculate -83 to the power of 2 and get 6889.

$$r^{2}=6889$$

Subtract 6889 from both sides.

$$r^{2}-6889=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -6889 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-6889\right)}}{2}$$

Square 0.

$$r=\frac{0±\sqrt{-4\left(-6889\right)}}{2}$$

Multiply -4 times -6889.

$$r=\frac{0±\sqrt{27556}}{2}$$

Take the square root of 27556.

$$r=\frac{0±166}{2}$$

Now solve the equation r=\frac{0±166}{2} when ± is plus. Divide 166 by 2.

$$r=83$$

Now solve the equation r=\frac{0±166}{2} when ± is minus. Divide -166 by 2.

$$r=-83$$

The equation is now solved.

$$r=83 r=-83$$