Solve 4r^2+64=100

$$4 r ^ { 2 } + 64 = 100$$

Solve for r

$$r=3$$

$$r=-3$$

Steps Using Difference of Squares

Subtract 100 from both sides.

$$4r^{2}+64-100=0$$

Subtract 100 from 64 to get -36.

$$4r^{2}-36=0$$

Divide both sides by 4.

$$r^{2}-9=0$$

Consider r^{2}-9. Rewrite r^{2}-9 as r^{2}-3^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(r-3\right)\left(r+3\right)=0$$

To find equation solutions, solve r-3=0 and r+3=0.

$$r=3 r=-3$$

Steps by Finding Square Root

Subtract 64 from both sides.

$$4r^{2}=100-64$$

Subtract 64 from 100 to get 36.

$$4r^{2}=36$$

Divide both sides by 4.

$$r^{2}=\frac{36}{4}$$

Divide 36 by 4 to get 9.

$$r^{2}=9$$

Take the square root of both sides of the equation.

$$r=3 r=-3$$

Steps Using the Quadratic Formula

Subtract 100 from both sides.

$$4r^{2}+64-100=0$$

Subtract 100 from 64 to get -36.

$$4r^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\times 4\left(-36\right)}}{2\times 4}$$

Square 0.

$$r=\frac{0±\sqrt{-4\times 4\left(-36\right)}}{2\times 4}$$

Multiply -4 times 4.

$$r=\frac{0±\sqrt{-16\left(-36\right)}}{2\times 4}$$

Multiply -16 times -36.

$$r=\frac{0±\sqrt{576}}{2\times 4}$$

Take the square root of 576.

$$r=\frac{0±24}{2\times 4}$$

Multiply 2 times 4.

$$r=\frac{0±24}{8}$$

Now solve the equation r=\frac{0±24}{8} when ± is plus. Divide 24 by 8.

$$r=3$$

Now solve the equation r=\frac{0±24}{8} when ± is minus. Divide -24 by 8.

$$r=-3$$

The equation is now solved.

$$r=3 r=-3$$