Solve (x-6)(x-10)=60

$$( x - 6 ) ( x - 10 ) = 60$$

Solve for x

$$x=16$$

$$x=0$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x-6 by x-10 and combine like terms.

$$x^{2}-16x+60=60$$

Subtract 60 from both sides.

$$x^{2}-16x+60-60=0$$

Subtract 60 from 60 to get 0.

$$x^{2}-16x=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -16 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-16\right)±\sqrt{\left(-16\right)^{2}}}{2}$$

Take the square root of \left(-16\right)^{2}.

$$x=\frac{-\left(-16\right)±16}{2}$$

The opposite of -16 is 16.

$$x=\frac{16±16}{2}$$

Now solve the equation x=\frac{16±16}{2} when ± is plus. Add 16 to 16.

$$x=\frac{32}{2}$$

Divide 32 by 2.

$$x=16$$

Now solve the equation x=\frac{16±16}{2} when ± is minus. Subtract 16 from 16.

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

Divide 0 by 2.

$$x=0$$

The equation is now solved.

$$x=16 x=0$$

Steps for Completing the Square

Use the distributive property to multiply x-6 by x-10 and combine like terms.

$$x^{2}-16x+60=60$$

Subtract 60 from both sides.

$$x^{2}-16x=60-60$$

Subtract 60 from 60 to get 0.

$$x^{2}-16x=0$$

Divide -16, the coefficient of the x term, by 2 to get -8. Then add the square of -8 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-16x+\left(-8\right)^{2}=\left(-8\right)^{2}$$

Square -8.

$$x^{2}-16x+64=64$$

Factor x^{2}-16x+64. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-8\right)^{2}=64$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-8\right)^{2}}=\sqrt{64}$$

Simplify.

$$x-8=8 x-8=-8$$

Add 8 to both sides of the equation.

$$x=16 x=0$$