Solve 50=4.9x^2

$$50 = 4.9 x ^ { 2 }$$

Solve for x

$$x = \frac{10 \sqrt{5}}{7} \approx 3.194382825$$

$$x = -\frac{10 \sqrt{5}}{7} \approx -3.194382825$$

Steps by Finding Square Root

Divide both sides by 4.9.

$$\frac{50}{4.9}=x^{2}$$

Expand \frac{50}{4.9} by multiplying both numerator and the denominator by 10.

$$\frac{500}{49}=x^{2}$$

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

$$x^{2}=\frac{500}{49}$$

Take the square root of both sides of the equation.

$$x=\frac{10\sqrt{5}}{7} x=-\frac{10\sqrt{5}}{7}$$

Steps Using the Quadratic Formula

Divide both sides by 4.9.

$$\frac{50}{4.9}=x^{2}$$

Expand \frac{50}{4.9} by multiplying both numerator and the denominator by 10.

$$\frac{500}{49}=x^{2}$$

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

$$x^{2}=\frac{500}{49}$$

Subtract \frac{500}{49} from both sides.

$$x^{2}-\frac{500}{49}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{500}{49} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{500}{49}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{500}{49}\right)}}{2}$$

Multiply -4 times -\frac{500}{49}.

$$x=\frac{0±\sqrt{\frac{2000}{49}}}{2}$$

Take the square root of \frac{2000}{49}.

$$x=\frac{0±\frac{20\sqrt{5}}{7}}{2}$$

Now solve the equation x=\frac{0±\frac{20\sqrt{5}}{7}}{2} when ± is plus.

$$x=\frac{10\sqrt{5}}{7}$$

Now solve the equation x=\frac{0±\frac{20\sqrt{5}}{7}}{2} when ± is minus.

$$x=-\frac{10\sqrt{5}}{7}$$

The equation is now solved.

$$x=\frac{10\sqrt{5}}{7} x=-\frac{10\sqrt{5}}{7}$$