Solve 81-r^2=0

$$81 - r ^ { 2 } = 0$$

Solve for r

$$r=9$$

$$r=-9$$

Steps by Finding Square Root

Subtract 81 from both sides. Anything subtracted from zero gives its negation.

$$-r^{2}=-81$$

Divide both sides by -1.

$$r^{2}=\frac{-81}{-1}$$

Fraction \frac{-81}{-1} can be simplified to 81 by removing the negative sign from both the numerator and the denominator.

$$r^{2}=81$$

Take the square root of both sides of the equation.

$$r=9 r=-9$$

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.

$$-r^{2}+81=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -1 for a, 0 for b, and 81 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-1\right)\times 81}}{2\left(-1\right)}$$

Square 0.

$$r=\frac{0±\sqrt{-4\left(-1\right)\times 81}}{2\left(-1\right)}$$

Multiply -4 times -1.

$$r=\frac{0±\sqrt{4\times 81}}{2\left(-1\right)}$$

Multiply 4 times 81.

$$r=\frac{0±\sqrt{324}}{2\left(-1\right)}$$

Take the square root of 324.

$$r=\frac{0±18}{2\left(-1\right)}$$

Multiply 2 times -1.

$$r=\frac{0±18}{-2}$$

Now solve the equation r=\frac{0±18}{-2} when ± is plus. Divide 18 by -2.

$$r=-9$$

Now solve the equation r=\frac{0±18}{-2} when ± is minus. Divide -18 by -2.

$$r=9$$

The equation is now solved.

$$r=-9 r=9$$