Solve (x-5)(x-2)=10

$$(x-5)(x-2)=10$$

Solve for x

$$x=7$$

$$x=0$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x-5 by x-2 and combine like terms.

$$x^{2}-7x+10=10$$

Subtract 10 from both sides.

$$x^{2}-7x+10-10=0$$

Subtract 10 from 10 to get 0.

$$x^{2}-7x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -7 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-7\right)±\sqrt{\left(-7\right)^{2}}}{2}$$

Take the square root of \left(-7\right)^{2}.

$$x=\frac{-\left(-7\right)±7}{2}$$

The opposite of -7 is 7.

$$x=\frac{7±7}{2}$$

Now solve the equation x=\frac{7±7}{2} when ± is plus. Add 7 to 7.

$$x=\frac{14}{2}$$

Divide 14 by 2.

$$x=7$$

Now solve the equation x=\frac{7±7}{2} when ± is minus. Subtract 7 from 7.

$$x=\frac{0}{2}$$

Divide 0 by 2.

$$x=0$$

The equation is now solved.

$$x=7 x=0$$

Steps for Completing the Square

Use the distributive property to multiply x-5 by x-2 and combine like terms.

$$x^{2}-7x+10=10$$

Subtract 10 from both sides.

$$x^{2}-7x=10-10$$

Subtract 10 from 10 to get 0.

$$x^{2}-7x=0$$

Divide -7, the coefficient of the x term, by 2 to get -\frac{7}{2}. Then add the square of -\frac{7}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-7x+\left(-\frac{7}{2}\right)^{2}=\left(-\frac{7}{2}\right)^{2}$$

Square -\frac{7}{2} by squaring both the numerator and the denominator of the fraction.

$$x^{2}-7x+\frac{49}{4}=\frac{49}{4}$$

Factor x^{2}-7x+\frac{49}{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}.

$$\left(x-\frac{7}{2}\right)^{2}=\frac{49}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-\frac{7}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Simplify.

$$x-\frac{7}{2}=\frac{7}{2} x-\frac{7}{2}=-\frac{7}{2}$$

Add \frac{7}{2} to both sides of the equation.

$$x=7 x=0$$