Solve r^2=0.586^2

$$r ^ { 2 } = 0.586 ^ { 2 }$$

Solve for r

$$r=0.586$$

$$r=-0.586$$

Steps Using Difference of Squares

Calculate 0.586 to the power of 2 and get 0.343396.

$$r^{2}=0.343396$$

Subtract 0.343396 from both sides.

$$r^{2}-0.343396=0$$

Consider r^{2}-0.343396. Rewrite r^{2}-0.343396 as r^{2}-\left(\frac{293}{500}\right)^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(r-\frac{293}{500}\right)\left(r+\frac{293}{500}\right)=0$$

To find equation solutions, solve r-\frac{293}{500}=0 and r+\frac{293}{500}=0.

$$r=\frac{293}{500} r=-0.586$$

Steps by Finding Square Root

Calculate 0.586 to the power of 2 and get 0.343396.

$$r^{2}=0.343396$$

Take the square root of both sides of the equation.

$$r=\frac{293}{500} r=-\frac{293}{500}$$

Steps Using the Quadratic Formula

Calculate 0.586 to the power of 2 and get 0.343396.

$$r^{2}=0.343396$$

Subtract 0.343396 from both sides.

$$r^{2}-0.343396=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -0.343396 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-0.343396\right)}}{2}$$

Square 0.

$$r=\frac{0±\sqrt{-4\left(-0.343396\right)}}{2}$$

Multiply -4 times -0.343396.

$$r=\frac{0±\sqrt{1.373584}}{2}$$

Take the square root of 1.373584.

$$r=\frac{0±\frac{293}{250}}{2}$$

Now solve the equation r=\frac{0±\frac{293}{250}}{2} when ± is plus.

$$r=\frac{293}{500}$$

Now solve the equation r=\frac{0±\frac{293}{250}}{2} when ± is minus.

$$r=-\frac{293}{500}$$

The equation is now solved.

$$r=\frac{293}{500} r=-\frac{293}{500}$$