Solve (x+2)(x)=300

$$( x + 2 ) ( x ) = 300$$

Solve for x (complex solution)

$$x=\sqrt{301}-1\approx 16.349351573$$

$$x=-\left(\sqrt{301}+1\right)\approx -18.349351573$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+2 by x.

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

Subtract 300 from both sides.

$$x^{2}+2x-300=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 2 for b, and -300 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 2.

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

Multiply -4 times -300.

$$x=\frac{-2±\sqrt{4+1200}}{2}$$

Add 4 to 1200.

$$x=\frac{-2±\sqrt{1204}}{2}$$

Take the square root of 1204.

$$x=\frac{-2±2\sqrt{301}}{2}$$

Now solve the equation x=\frac{-2±2\sqrt{301}}{2} when ± is plus. Add -2 to 2\sqrt{301}.

$$x=\frac{2\sqrt{301}-2}{2}$$

Divide -2+2\sqrt{301} by 2.

$$x=\sqrt{301}-1$$

Now solve the equation x=\frac{-2±2\sqrt{301}}{2} when ± is minus. Subtract 2\sqrt{301} from -2.

$$x=\frac{-2\sqrt{301}-2}{2}$$

Divide -2-2\sqrt{301} by 2.

$$x=-\sqrt{301}-1$$

The equation is now solved.

$$x=\sqrt{301}-1 x=-\sqrt{301}-1$$

Steps for Completing the Square

Use the distributive property to multiply x+2 by x.

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

Divide 2, the coefficient of the x term, by 2 to get 1. Then add the square of 1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+2x+1^{2}=300+1^{2}$$

Square 1.

$$x^{2}+2x+1=300+1$$

Add 300 to 1.

$$x^{2}+2x+1=301$$

Factor x^{2}+2x+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+1\right)^{2}=301$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{301}$$

Simplify.

$$x+1=\sqrt{301} x+1=-\sqrt{301}$$

Subtract 1 from both sides of the equation.

$$x=\sqrt{301}-1 x=-\sqrt{301}-1$$

Solve for x

$$x=\sqrt{301}-1\approx 16.349351573$$

$$x=-\sqrt{301}-1\approx -18.349351573$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x+2 by x.

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

Subtract 300 from both sides.

$$x^{2}+2x-300=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 2 for b, and -300 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

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

Square 2.

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

Multiply -4 times -300.

$$x=\frac{-2±\sqrt{4+1200}}{2}$$

Add 4 to 1200.

$$x=\frac{-2±\sqrt{1204}}{2}$$

Take the square root of 1204.

$$x=\frac{-2±2\sqrt{301}}{2}$$

Now solve the equation x=\frac{-2±2\sqrt{301}}{2} when ± is plus. Add -2 to 2\sqrt{301}.

$$x=\frac{2\sqrt{301}-2}{2}$$

Divide -2+2\sqrt{301} by 2.

$$x=\sqrt{301}-1$$

Now solve the equation x=\frac{-2±2\sqrt{301}}{2} when ± is minus. Subtract 2\sqrt{301} from -2.

$$x=\frac{-2\sqrt{301}-2}{2}$$

Divide -2-2\sqrt{301} by 2.

$$x=-\sqrt{301}-1$$

The equation is now solved.

$$x=\sqrt{301}-1 x=-\sqrt{301}-1$$

Steps for Completing the Square

Use the distributive property to multiply x+2 by x.

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

Divide 2, the coefficient of the x term, by 2 to get 1. Then add the square of 1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}+2x+1^{2}=300+1^{2}$$

Square 1.

$$x^{2}+2x+1=300+1$$

Add 300 to 1.

$$x^{2}+2x+1=301$$

Factor x^{2}+2x+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x+1\right)^{2}=301$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{301}$$

Simplify.

$$x+1=\sqrt{301} x+1=-\sqrt{301}$$

Subtract 1 from both sides of the equation.

$$x=\sqrt{301}-1 x=-\sqrt{301}-1$$