Solve 4=(x-300)(x-300)

$$4=(x-300)(x-300)$$

Solve for x

$$x=302$$

$$x=298$$

Steps Using the Quadratic Formula

Multiply x-300 and x-300 to get \left(x-300\right)^{2}.

$$4=\left(x-300\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-300\right)^{2}.

$$4=x^{2}-600x+90000$$

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

$$x^{2}-600x+90000=4$$

Subtract 4 from both sides.

$$x^{2}-600x+90000-4=0$$

Subtract 4 from 90000 to get 89996.

$$x^{2}-600x+89996=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -600 for b, and 89996 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-600\right)±\sqrt{\left(-600\right)^{2}-4\times 89996}}{2}$$

Square -600.

$$x=\frac{-\left(-600\right)±\sqrt{360000-4\times 89996}}{2}$$

Multiply -4 times 89996.

$$x=\frac{-\left(-600\right)±\sqrt{360000-359984}}{2}$$

Add 360000 to -359984.

$$x=\frac{-\left(-600\right)±\sqrt{16}}{2}$$

Take the square root of 16.

$$x=\frac{-\left(-600\right)±4}{2}$$

The opposite of -600 is 600.

$$x=\frac{600±4}{2}$$

Now solve the equation x=\frac{600±4}{2} when ± is plus. Add 600 to 4.

$$x=\frac{604}{2}$$

Divide 604 by 2.

$$x=302$$

Now solve the equation x=\frac{600±4}{2} when ± is minus. Subtract 4 from 600.

$$x=\frac{596}{2}$$

Divide 596 by 2.

$$x=298$$

The equation is now solved.

$$x=302 x=298$$

Steps for Completing the Square

Multiply x-300 and x-300 to get \left(x-300\right)^{2}.

$$4=\left(x-300\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-300\right)^{2}.

$$4=x^{2}-600x+90000$$

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

$$x^{2}-600x+90000=4$$

Factor x^{2}-600x+90000. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-300\right)^{2}=4$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-300\right)^{2}}=\sqrt{4}$$

Simplify.

$$x-300=2 x-300=-2$$

Add 300 to both sides of the equation.

$$x=302 x=298$$