Solve x^2+(600)^2+600x=3x^2

$$x ^ { 2 } + ( 600 ) ^ { 2 } + 600 x = 3 x ^ { 2 }$$

Solve for x

$$x=-300$$

$$x=600$$

Steps Using the Quadratic Formula

Calculate 600 to the power of 2 and get 360000.

$$x^{2}+360000+600x=3x^{2}$$

Subtract 3x^{2} from both sides.

$$x^{2}+360000+600x-3x^{2}=0$$

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

$$-2x^{2}+360000+600x=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$-2x^{2}+600x+360000=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -2 for a, 600 for b, and 360000 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-600±\sqrt{600^{2}-4\left(-2\right)\times 360000}}{2\left(-2\right)}$$

Square 600.

$$x=\frac{-600±\sqrt{360000-4\left(-2\right)\times 360000}}{2\left(-2\right)}$$

Multiply -4 times -2.

$$x=\frac{-600±\sqrt{360000+8\times 360000}}{2\left(-2\right)}$$

Multiply 8 times 360000.

$$x=\frac{-600±\sqrt{360000+2880000}}{2\left(-2\right)}$$

Add 360000 to 2880000.

$$x=\frac{-600±\sqrt{3240000}}{2\left(-2\right)}$$

Take the square root of 3240000.

$$x=\frac{-600±1800}{2\left(-2\right)}$$

Multiply 2 times -2.

$$x=\frac{-600±1800}{-4}$$

Now solve the equation x=\frac{-600±1800}{-4} when ± is plus. Add -600 to 1800.

$$x=\frac{1200}{-4}$$

Divide 1200 by -4.

$$x=-300$$

Now solve the equation x=\frac{-600±1800}{-4} when ± is minus. Subtract 1800 from -600.

$$x=-\frac{2400}{-4}$$

Divide -2400 by -4.

$$x=600$$

The equation is now solved.

$$x=-300 x=600$$

Steps for Completing the Square

Calculate 600 to the power of 2 and get 360000.

$$x^{2}+360000+600x=3x^{2}$$

Subtract 3x^{2} from both sides.

$$x^{2}+360000+600x-3x^{2}=0$$

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

$$-2x^{2}+360000+600x=0$$

Subtract 360000 from both sides. Anything subtracted from zero gives its negation.

$$-2x^{2}+600x=-360000$$

Divide both sides by -2.

$$\frac{-2x^{2}+600x}{-2}=-\frac{360000}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x^{2}+\frac{600}{-2}x=-\frac{360000}{-2}$$

Divide 600 by -2.

$$x^{2}-300x=-\frac{360000}{-2}$$

Divide -360000 by -2.

$$x^{2}-300x=180000$$

Divide -300, the coefficient of the x term, by 2 to get -150. Then add the square of -150 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-300x+\left(-150\right)^{2}=180000+\left(-150\right)^{2}$$

Square -150.

$$x^{2}-300x+22500=180000+22500$$

Add 180000 to 22500.

$$x^{2}-300x+22500=202500$$

Factor x^{2}-300x+22500. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-150\right)^{2}=202500$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-150\right)^{2}}=\sqrt{202500}$$

Simplify.

$$x-150=450 x-150=-450$$

Add 150 to both sides of the equation.

$$x=600 x=-300$$