Solve r^2=(-.83)^2

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

Solve for r

$$r=0.83$$

$$r=-0.83$$

Steps Using Difference of Squares

Calculate -0.83 to the power of 2 and get 0.6889.

$$r^{2}=0.6889$$

Subtract 0.6889 from both sides.

$$r^{2}-0.6889=0$$

Consider r^{2}-0.6889. Rewrite r^{2}-0.6889 as r^{2}-\left(\frac{83}{100}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(r-\frac{83}{100}\right)\left(r+\frac{83}{100}\right)=0$$

To find equation solutions, solve r-\frac{83}{100}=0 and r+\frac{83}{100}=0.

$$r=0.83 r=-0.83$$

Steps by Finding Square Root

Calculate -0.83 to the power of 2 and get 0.6889.

$$r^{2}=0.6889$$

Take the square root of both sides of the equation.

$$r=\frac{83}{100} r=-\frac{83}{100}$$

Steps Using the Quadratic Formula

Calculate -0.83 to the power of 2 and get 0.6889.

$$r^{2}=0.6889$$

Subtract 0.6889 from both sides.

$$r^{2}-0.6889=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -0.6889 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-0.6889\right)}}{2}$$

Square 0.

$$r=\frac{0±\sqrt{-4\left(-0.6889\right)}}{2}$$

Multiply -4 times -0.6889.

$$r=\frac{0±\sqrt{2.7556}}{2}$$

Take the square root of 2.7556.

$$r=\frac{0±\frac{83}{50}}{2}$$

Now solve the equation r=\frac{0±\frac{83}{50}}{2} when ± is plus.

$$r=\frac{83}{100}$$

Now solve the equation r=\frac{0±\frac{83}{50}}{2} when ± is minus.

$$r=-\frac{83}{100}$$

The equation is now solved.

$$r=\frac{83}{100} r=-\frac{83}{100}$$