Solve -4r^2+48=-164

$$- 4 r ^ { 2 } + 48 = - 164$$

Solve for r

$$r=\sqrt{53}\approx 7.280109889$$

$$r=-\sqrt{53}\approx -7.280109889$$

Steps by Finding Square Root

Subtract 48 from both sides.

$$-4r^{2}=-164-48$$

Subtract 48 from -164 to get -212.

$$-4r^{2}=-212$$

Divide both sides by -4.

$$r^{2}=\frac{-212}{-4}$$

Divide -212 by -4 to get 53.

$$r^{2}=53$$

Take the square root of both sides of the equation.

$$r=\sqrt{53} r=-\sqrt{53}$$

Steps Using the Quadratic Formula

Add 164 to both sides.

$$-4r^{2}+48+164=0$$

Add 48 and 164 to get 212.

$$-4r^{2}+212=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -4 for a, 0 for b, and 212 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\left(-4\right)\times 212}}{2\left(-4\right)}$$

Square 0.

$$r=\frac{0±\sqrt{-4\left(-4\right)\times 212}}{2\left(-4\right)}$$

Multiply -4 times -4.

$$r=\frac{0±\sqrt{16\times 212}}{2\left(-4\right)}$$

Multiply 16 times 212.

$$r=\frac{0±\sqrt{3392}}{2\left(-4\right)}$$

Take the square root of 3392.

$$r=\frac{0±8\sqrt{53}}{2\left(-4\right)}$$

Multiply 2 times -4.

$$r=\frac{0±8\sqrt{53}}{-8}$$

Now solve the equation r=\frac{0±8\sqrt{53}}{-8} when ± is plus.

$$r=-\sqrt{53}$$

Now solve the equation r=\frac{0±8\sqrt{53}}{-8} when ± is minus.

$$r=\sqrt{53}$$

The equation is now solved.

$$r=-\sqrt{53} r=\sqrt{53}$$