Solve 382=0.5*9*x^2

$$382 = 0.5 \times 9 \times { x }^{ 2 }$$

Solve for x

$$x = \frac{2 \sqrt{191}}{3} \approx 9.213516641$$

$$x = -\frac{2 \sqrt{191}}{3} \approx -9.213516641$$

Steps by Finding Square Root

Multiply 0.5 and 9 to get 4.5.

$$382=4.5x^{2}$$

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

$$4.5x^{2}=382$$

Divide both sides by 4.5.

$$x^{2}=\frac{382}{4.5}$$

Expand \frac{382}{4.5} by multiplying both numerator and the denominator by 10.

$$x^{2}=\frac{3820}{45}$$

Reduce the fraction \frac{3820}{45} to lowest terms by extracting and canceling out 5.

$$x^{2}=\frac{764}{9}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{191}}{3} x=-\frac{2\sqrt{191}}{3}$$

Steps Using the Quadratic Formula

Multiply 0.5 and 9 to get 4.5.

$$382=4.5x^{2}$$

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

$$4.5x^{2}=382$$

Subtract 382 from both sides.

$$4.5x^{2}-382=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4.5 for a, 0 for b, and -382 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4.5\left(-382\right)}}{2\times 4.5}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4.5\left(-382\right)}}{2\times 4.5}$$

Multiply -4 times 4.5.

$$x=\frac{0±\sqrt{-18\left(-382\right)}}{2\times 4.5}$$

Multiply -18 times -382.

$$x=\frac{0±\sqrt{6876}}{2\times 4.5}$$

Take the square root of 6876.

$$x=\frac{0±6\sqrt{191}}{2\times 4.5}$$

Multiply 2 times 4.5.

$$x=\frac{0±6\sqrt{191}}{9}$$

Now solve the equation x=\frac{0±6\sqrt{191}}{9} when ± is plus.

$$x=\frac{2\sqrt{191}}{3}$$

Now solve the equation x=\frac{0±6\sqrt{191}}{9} when ± is minus.

$$x=-\frac{2\sqrt{191}}{3}$$

The equation is now solved.

$$x=\frac{2\sqrt{191}}{3} x=-\frac{2\sqrt{191}}{3}$$