Solve 600=(2x+4)(x-3)

$$600 = ( 2 x + 4 ) ( x - 3 )$$

Solve for x

$$x=-17$$

$$x=18$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 2x+4 by x-3 and combine like terms.

$$600=2x^{2}-2x-12$$

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

$$2x^{2}-2x-12=600$$

Subtract 600 from both sides.

$$2x^{2}-2x-12-600=0$$

Subtract 600 from -12 to get -612.

$$2x^{2}-2x-612=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, -2 for b, and -612 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\times 2\left(-612\right)}}{2\times 2}$$

Square -2.

$$x=\frac{-\left(-2\right)±\sqrt{4-4\times 2\left(-612\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{-\left(-2\right)±\sqrt{4-8\left(-612\right)}}{2\times 2}$$

Multiply -8 times -612.

$$x=\frac{-\left(-2\right)±\sqrt{4+4896}}{2\times 2}$$

Add 4 to 4896.

$$x=\frac{-\left(-2\right)±\sqrt{4900}}{2\times 2}$$

Take the square root of 4900.

$$x=\frac{-\left(-2\right)±70}{2\times 2}$$

The opposite of -2 is 2.

$$x=\frac{2±70}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{2±70}{4}$$

Now solve the equation x=\frac{2±70}{4} when ± is plus. Add 2 to 70.

$$x=\frac{72}{4}$$

Divide 72 by 4.

$$x=18$$

Now solve the equation x=\frac{2±70}{4} when ± is minus. Subtract 70 from 2.

$$x=-\frac{68}{4}$$

Divide -68 by 4.

$$x=-17$$

The equation is now solved.

$$x=18 x=-17$$

Steps for Completing the Square

Use the distributive property to multiply 2x+4 by x-3 and combine like terms.

$$600=2x^{2}-2x-12$$

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

$$2x^{2}-2x-12=600$$

Add 12 to both sides.

$$2x^{2}-2x=600+12$$

Add 600 and 12 to get 612.

$$2x^{2}-2x=612$$

Divide both sides by 2.

$$\frac{2x^{2}-2x}{2}=\frac{612}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}+\left(-\frac{2}{2}\right)x=\frac{612}{2}$$

Divide -2 by 2.

$$x^{2}-x=\frac{612}{2}$$

Divide 612 by 2.

$$x^{2}-x=306$$

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

$$x^{2}-x+\left(-\frac{1}{2}\right)^{2}=306+\left(-\frac{1}{2}\right)^{2}$$

Square -\frac{1}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-x+\frac{1}{4}=306+\frac{1}{4}$$

Add 306 to \frac{1}{4}.

$$x^{2}-x+\frac{1}{4}=\frac{1225}{4}$$

Factor x^{2}-x+\frac{1}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-\frac{1}{2}\right)^{2}=\frac{1225}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{1}{2}\right)^{2}}=\sqrt{\frac{1225}{4}}$$

Simplify.

$$x-\frac{1}{2}=\frac{35}{2} x-\frac{1}{2}=-\frac{35}{2}$$

Add \frac{1}{2} to both sides of the equation.

$$x=18 x=-17$$