Solve (x)(x+2)=624

$$( x ) ( x + 2 ) = 624$$

Solve for x

$$x=-26$$

$$x=24$$

Steps Using the Quadratic Formula

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

$$x^{2}+2x=624$$

Subtract 624 from both sides.

$$x^{2}+2x-624=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 2 for b, and -624 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-2±\sqrt{2^{2}-4\left(-624\right)}}{2}$$

Square 2.

$$x=\frac{-2±\sqrt{4-4\left(-624\right)}}{2}$$

Multiply -4 times -624.

$$x=\frac{-2±\sqrt{4+2496}}{2}$$

Add 4 to 2496.

$$x=\frac{-2±\sqrt{2500}}{2}$$

Take the square root of 2500.

$$x=\frac{-2±50}{2}$$

Now solve the equation x=\frac{-2±50}{2} when ± is plus. Add -2 to 50.

$$x=\frac{48}{2}$$

Divide 48 by 2.

$$x=24$$

Now solve the equation x=\frac{-2±50}{2} when ± is minus. Subtract 50 from -2.

$$x=-\frac{52}{2}$$

Divide -52 by 2.

$$x=-26$$

The equation is now solved.

$$x=24 x=-26$$

Steps for Completing the Square

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

$$x^{2}+2x=624$$

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.

$$x^{2}+2x+1^{2}=624+1^{2}$$

Square 1.

$$x^{2}+2x+1=624+1$$

Add 624 to 1.

$$x^{2}+2x+1=625$$

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}.

$$\left(x+1\right)^{2}=625$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x+1\right)^{2}}=\sqrt{625}$$

Simplify.

$$x+1=25 x+1=-25$$

Subtract 1 from both sides of the equation.

$$x=24 x=-26$$