Solve 3+1.2=1/2*9.8r^2

$$3 + 1.2 = \frac { 1 } { 2 } \times 9.8 r ^ { 2 }$$

Solve for r

$$r=\frac{\sqrt{42}}{7}\approx 0.9258201$$

$$r=-\frac{\sqrt{42}}{7}\approx -0.9258201$$

Steps by Finding Square Root

Add 3 and 1.2 to get 4.2.

$$4.2=\frac{1}{2}\times 9.8r^{2}$$

Multiply \frac{1}{2} and 9.8 to get \frac{49}{10}.

$$4.2=\frac{49}{10}r^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{49}{10}r^{2}=4.2$$

Multiply both sides by \frac{10}{49}, the reciprocal of \frac{49}{10}.

$$r^{2}=4.2\times \frac{10}{49}$$

Multiply 4.2 and \frac{10}{49} to get \frac{6}{7}.

$$r^{2}=\frac{6}{7}$$

Take the square root of both sides of the equation.

$$r=\frac{\sqrt{42}}{7} r=-\frac{\sqrt{42}}{7}$$

Steps Using the Quadratic Formula

Add 3 and 1.2 to get 4.2.

$$4.2=\frac{1}{2}\times 9.8r^{2}$$

Multiply \frac{1}{2} and 9.8 to get \frac{49}{10}.

$$4.2=\frac{49}{10}r^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{49}{10}r^{2}=4.2$$

Subtract 4.2 from both sides.

$$\frac{49}{10}r^{2}-4.2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute \frac{49}{10} for a, 0 for b, and -4.2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$r=\frac{0±\sqrt{0^{2}-4\times \frac{49}{10}\left(-4.2\right)}}{2\times \frac{49}{10}}$$

Square 0.

$$r=\frac{0±\sqrt{-4\times \frac{49}{10}\left(-4.2\right)}}{2\times \frac{49}{10}}$$

Multiply -4 times \frac{49}{10}.

$$r=\frac{0±\sqrt{-\frac{98}{5}\left(-4.2\right)}}{2\times \frac{49}{10}}$$

Multiply -\frac{98}{5} times -4.2 by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$r=\frac{0±\sqrt{\frac{2058}{25}}}{2\times \frac{49}{10}}$$

Take the square root of \frac{2058}{25}.

$$r=\frac{0±\frac{7\sqrt{42}}{5}}{2\times \frac{49}{10}}$$

Multiply 2 times \frac{49}{10}.

$$r=\frac{0±\frac{7\sqrt{42}}{5}}{\frac{49}{5}}$$

Now solve the equation r=\frac{0±\frac{7\sqrt{42}}{5}}{\frac{49}{5}} when ± is plus.

$$r=\frac{\sqrt{42}}{7}$$

Now solve the equation r=\frac{0±\frac{7\sqrt{42}}{5}}{\frac{49}{5}} when ± is minus.

$$r=-\frac{\sqrt{42}}{7}$$

The equation is now solved.

$$r=\frac{\sqrt{42}}{7} r=-\frac{\sqrt{42}}{7}$$