Solve (x-8)(x-6)=-1

$$( x - 8 ) ( x - 6 ) = - 1$$

Solve for x

$$x=7$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x-8 by x-6 and combine like terms.

$$x^{2}-14x+48=-1$$

Add 1 to both sides.

$$x^{2}-14x+48+1=0$$

Add 48 and 1 to get 49.

$$x^{2}-14x+49=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -14 for b, and 49 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{-\left(-14\right)±\sqrt{\left(-14\right)^{2}-4\times 49}}{2}$$

Square -14.

$$x=\frac{-\left(-14\right)±\sqrt{196-4\times 49}}{2}$$

Multiply -4 times 49.

$$x=\frac{-\left(-14\right)±\sqrt{196-196}}{2}$$

Add 196 to -196.

$$x=\frac{-\left(-14\right)±\sqrt{0}}{2}$$

Take the square root of 0.

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

The opposite of -14 is 14.

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

Divide 14 by 2.

$$x=7$$

Steps for Completing the Square

Use the distributive property to multiply x-8 by x-6 and combine like terms.

$$x^{2}-14x+48=-1$$

Subtract 48 from both sides.

$$x^{2}-14x=-1-48$$

Subtract 48 from -1 to get -49.

$$x^{2}-14x=-49$$

Divide -14, the coefficient of the x term, by 2 to get -7. Then add the square of -7 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-14x+\left(-7\right)^{2}=-49+\left(-7\right)^{2}$$

Square -7.

$$x^{2}-14x+49=-49+49$$

Add -49 to 49.

$$x^{2}-14x+49=0$$

Factor x^{2}-14x+49. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-7\right)^{2}=0$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-7\right)^{2}}=\sqrt{0}$$

Simplify.

$$x-7=0 x-7=0$$

Add 7 to both sides of the equation.

$$x=7 x=7$$

The equation is now solved. Solutions are the same.

$$x=7$$