Solve 4.48r^2+4.48-5.1968=0

$$4.48 r ^ { 2 } + 4.48 - 5.1968 = 0$$

Solve for r

$$r=0.4$$

$$r=-0.4$$

Steps by Finding Square Root

Subtract 5.1968 from 4.48 to get -0.7168.

$$4.48r^{2}-0.7168=0$$

Add 0.7168 to both sides. Anything plus zero gives itself.

$$4.48r^{2}=0.7168$$

Divide both sides by 4.48.

$$r^{2}=\frac{0.7168}{4.48}$$

Expand \frac{0.7168}{4.48} by multiplying both numerator and the denominator by 10000.

$$r^{2}=\frac{7168}{44800}$$

Reduce the fraction \frac{7168}{44800} to lowest terms by extracting and canceling out 1792.

$$r^{2}=\frac{4}{25}$$

Take the square root of both sides of the equation.

$$r=\frac{2}{5} r=-\frac{2}{5}$$

Steps Using the Quadratic Formula

Subtract 5.1968 from 4.48 to get -0.7168.

$$4.48r^{2}-0.7168=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4.48 for a, 0 for b, and -0.7168 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\times 4.48\left(-0.7168\right)}}{2\times 4.48}$$

Square 0.

$$r=\frac{0±\sqrt{-4\times 4.48\left(-0.7168\right)}}{2\times 4.48}$$

Multiply -4 times 4.48.

$$r=\frac{0±\sqrt{-17.92\left(-0.7168\right)}}{2\times 4.48}$$

Multiply -17.92 times -0.7168 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$r=\frac{0±\sqrt{12.845056}}{2\times 4.48}$$

Take the square root of 12.845056.

$$r=\frac{0±\frac{448}{125}}{2\times 4.48}$$

Multiply 2 times 4.48.

$$r=\frac{0±\frac{448}{125}}{8.96}$$

Now solve the equation r=\frac{0±\frac{448}{125}}{8.96} when ± is plus.

$$r=\frac{2}{5}$$

Now solve the equation r=\frac{0±\frac{448}{125}}{8.96} when ± is minus.

$$r=-\frac{2}{5}$$

The equation is now solved.

$$r=\frac{2}{5} r=-\frac{2}{5}$$