Solve x^2-120x+3600=0

$${ x }^{ 2 } -120x+3600=0$$

Solve for x

$$x=60$$

Steps Using the Quadratic Formula

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.

$$x^{2}-120x+3600=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -120 for b, and 3600 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-120\right)±\sqrt{\left(-120\right)^{2}-4\times 3600}}{2}$$

Square -120.

$$x=\frac{-\left(-120\right)±\sqrt{14400-4\times 3600}}{2}$$

Multiply -4 times 3600.

$$x=\frac{-\left(-120\right)±\sqrt{14400-14400}}{2}$$

Add 14400 to -14400.

$$x=\frac{-\left(-120\right)±\sqrt{0}}{2}$$

Take the square root of 0.

$$x=-\frac{-120}{2}$$

The opposite of -120 is 120.

$$x=\frac{120}{2}$$

Divide 120 by 2.

$$x=60$$

Steps for Completing the Square

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$x^{2}-120x+3600=0$$

Factor x^{2}-120x+3600. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-60\right)^{2}=0$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-60\right)^{2}}=\sqrt{0}$$

Simplify.

$$x-60=0 x-60=0$$

Add 60 to both sides of the equation.

$$x=60 x=60$$

The equation is now solved. Solutions are the same.

$$x=60$$