Solve (x-8)(x-3)=2+2x,w

$$( x - 8 ) ( x - 3 ) = 2 + 2 x , w$$

Solve for x

$$x=2$$

$$x=11$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x-8 by x-3 and combine like terms.

$$x^{2}-11x+24=2+2x$$

Subtract 2 from both sides.

$$x^{2}-11x+24-2=2x$$

Subtract 2 from 24 to get 22.

$$x^{2}-11x+22=2x$$

Subtract 2x from both sides.

$$x^{2}-11x+22-2x=0$$

Combine -11x and -2x to get -13x.

$$x^{2}-13x+22=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -13 for b, and 22 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-13\right)±\sqrt{\left(-13\right)^{2}-4\times 22}}{2}$$

Square -13.

$$x=\frac{-\left(-13\right)±\sqrt{169-4\times 22}}{2}$$

Multiply -4 times 22.

$$x=\frac{-\left(-13\right)±\sqrt{169-88}}{2}$$

Add 169 to -88.

$$x=\frac{-\left(-13\right)±\sqrt{81}}{2}$$

Take the square root of 81.

$$x=\frac{-\left(-13\right)±9}{2}$$

The opposite of -13 is 13.

$$x=\frac{13±9}{2}$$

Now solve the equation x=\frac{13±9}{2} when ± is plus. Add 13 to 9.

$$x=\frac{22}{2}$$

Divide 22 by 2.

$$x=11$$

Now solve the equation x=\frac{13±9}{2} when ± is minus. Subtract 9 from 13.

$$x=\frac{4}{2}$$

Divide 4 by 2.

$$x=2$$

The equation is now solved.

$$x=11 x=2$$

Steps for Completing the Square

Use the distributive property to multiply x-8 by x-3 and combine like terms.

$$x^{2}-11x+24=2+2x$$

Subtract 2x from both sides.

$$x^{2}-11x+24-2x=2$$

Combine -11x and -2x to get -13x.

$$x^{2}-13x+24=2$$

Subtract 24 from both sides.

$$x^{2}-13x=2-24$$

Subtract 24 from 2 to get -22.

$$x^{2}-13x=-22$$

Divide -13, the coefficient of the x term, by 2 to get -\frac{13}{2}. Then add the square of -\frac{13}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-13x+\left(-\frac{13}{2}\right)^{2}=-22+\left(-\frac{13}{2}\right)^{2}$$

Square -\frac{13}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-13x+\frac{169}{4}=-22+\frac{169}{4}$$

Add -22 to \frac{169}{4}.

$$x^{2}-13x+\frac{169}{4}=\frac{81}{4}$$

Factor x^{2}-13x+\frac{169}{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}.

$$\left(x-\frac{13}{2}\right)^{2}=\frac{81}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{13}{2}\right)^{2}}=\sqrt{\frac{81}{4}}$$

Simplify.

$$x-\frac{13}{2}=\frac{9}{2} x-\frac{13}{2}=-\frac{9}{2}$$

Add \frac{13}{2} to both sides of the equation.

$$x=11 x=2$$