Solve 480000=36300x^2

$$480000=36300 { x }^{ 2 }$$

Solve for x

$$x = \frac{40}{11} = 3\frac{7}{11} \approx 3.636363636$$

$$x = -\frac{40}{11} = -3\frac{7}{11} \approx -3.636363636$$

Steps Using Difference of Squares

Divide both sides by 36300.

$$\frac{480000}{36300}=x^{2}$$

Reduce the fraction \frac{480000}{36300} to lowest terms by extracting and canceling out 300.

$$\frac{1600}{121}=x^{2}$$

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

$$x^{2}=\frac{1600}{121}$$

Subtract \frac{1600}{121} from both sides.

$$x^{2}-\frac{1600}{121}=0$$

Multiply both sides by 121.

$$121x^{2}-1600=0$$

Consider 121x^{2}-1600. Rewrite 121x^{2}-1600 as \left(11x\right)^{2}-40^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(11x-40\right)\left(11x+40\right)=0$$

To find equation solutions, solve 11x-40=0 and 11x+40=0.

$$x=\frac{40}{11} x=-\frac{40}{11}$$

Steps by Finding Square Root

Divide both sides by 36300.

$$\frac{480000}{36300}=x^{2}$$

Reduce the fraction \frac{480000}{36300} to lowest terms by extracting and canceling out 300.

$$\frac{1600}{121}=x^{2}$$

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

$$x^{2}=\frac{1600}{121}$$

Take the square root of both sides of the equation.

$$x=\frac{40}{11} x=-\frac{40}{11}$$

Steps Using the Quadratic Formula

Divide both sides by 36300.

$$\frac{480000}{36300}=x^{2}$$

Reduce the fraction \frac{480000}{36300} to lowest terms by extracting and canceling out 300.

$$\frac{1600}{121}=x^{2}$$

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

$$x^{2}=\frac{1600}{121}$$

Subtract \frac{1600}{121} from both sides.

$$x^{2}-\frac{1600}{121}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{1600}{121} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{1600}{121}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{1600}{121}\right)}}{2}$$

Multiply -4 times -\frac{1600}{121}.

$$x=\frac{0±\sqrt{\frac{6400}{121}}}{2}$$

Take the square root of \frac{6400}{121}.

$$x=\frac{0±\frac{80}{11}}{2}$$

Now solve the equation x=\frac{0±\frac{80}{11}}{2} when ± is plus.

$$x=\frac{40}{11}$$

Now solve the equation x=\frac{0±\frac{80}{11}}{2} when ± is minus.

$$x=-\frac{40}{11}$$

The equation is now solved.

$$x=\frac{40}{11} x=-\frac{40}{11}$$