Solve (300-2x^2+600^2=x^2

$$( 300 - 2 x ^ { 2 } + 600 ^ { 2 } = x ^ { 2 }$$

Solve for x

$$x=10\sqrt{1201}\approx 346.554469023$$

$$x=-10\sqrt{1201}\approx -346.554469023$$

Steps by Finding Square Root

Calculate 600 to the power of 2 and get 360000.

$$300-2x^{2}+360000=x^{2}$$

Add 300 and 360000 to get 360300.

$$360300-2x^{2}=x^{2}$$

Subtract x^{2} from both sides.

$$360300-2x^{2}-x^{2}=0$$

Combine -2x^{2} and -x^{2} to get -3x^{2}.

$$360300-3x^{2}=0$$

Subtract 360300 from both sides. Anything subtracted from zero gives its negation.

$$-3x^{2}=-360300$$

Divide both sides by -3.

$$x^{2}=\frac{-360300}{-3}$$

Divide -360300 by -3 to get 120100.

$$x^{2}=120100$$

Take the square root of both sides of the equation.

$$x=10\sqrt{1201} x=-10\sqrt{1201}$$

Steps Using the Quadratic Formula

Calculate 600 to the power of 2 and get 360000.

$$300-2x^{2}+360000=x^{2}$$

Add 300 and 360000 to get 360300.

$$360300-2x^{2}=x^{2}$$

Subtract x^{2} from both sides.

$$360300-2x^{2}-x^{2}=0$$

Combine -2x^{2} and -x^{2} to get -3x^{2}.

$$360300-3x^{2}=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$-3x^{2}+360300=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -3 for a, 0 for b, and 360300 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-3\right)\times 360300}}{2\left(-3\right)}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-3\right)\times 360300}}{2\left(-3\right)}$$

Multiply -4 times -3.

$$x=\frac{0±\sqrt{12\times 360300}}{2\left(-3\right)}$$

Multiply 12 times 360300.

$$x=\frac{0±\sqrt{4323600}}{2\left(-3\right)}$$

Take the square root of 4323600.

$$x=\frac{0±60\sqrt{1201}}{2\left(-3\right)}$$

Multiply 2 times -3.

$$x=\frac{0±60\sqrt{1201}}{-6}$$

Now solve the equation x=\frac{0±60\sqrt{1201}}{-6} when ± is plus.

$$x=-10\sqrt{1201}$$

Now solve the equation x=\frac{0±60\sqrt{1201}}{-6} when ± is minus.

$$x=10\sqrt{1201}$$

The equation is now solved.

$$x=-10\sqrt{1201} x=10\sqrt{1201}$$