Solve Using the Quadratic Formula (x-8)(x-10)=-1

$(x - 8) (x - 10) = - 1$

Step 1

Move all terms to the left side of the equation and simplify.

Simplify the left side.

Simplify $(x - 8) (x - 10)$ .

Expand $(x - 8) (x - 10)$ using the FOIL Method.

Apply the distributive property.

$x (x - 10) - 8 (x - 10) = - 1$

Apply the distributive property.

$x \cdot x + x \cdot - 10 - 8 (x - 10) = - 1$

Apply the distributive property.

$x \cdot x + x \cdot - 10 - 8 x - 8 \cdot - 10 = - 1$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 10 - 8 x - 8 \cdot - 10 = - 1$

Move $- 10$ to the left of $x$ .

$x^{2} - 10 \cdot x - 8 x - 8 \cdot - 10 = - 1$

Multiply $- 8$ by $- 10$ .

$x^{2} - 10 x - 8 x + 80 = - 1$

Subtract $8 x$ from $- 10 x$ .

$x^{2} - 18 x + 80 = - 1$

Add $1$ to both sides of the equation.

$x^{2} - 18 x + 80 + 1 = 0$

Add $80$ and $1$ .

$x^{2} - 18 x + 81 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = - 18$ , and $c = 81$ into the quadratic formula and solve for $x$ .

$\frac{18 \pm \sqrt{{(- 18)}^{2} - 4 \cdot (1 \cdot 81)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 18$ to the power of $2$ .

$x = \frac{18 \pm \sqrt{324 - 4 \cdot 1 \cdot 81}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 81$ .

Multiply $- 4$ by $1$ .

$x = \frac{18 \pm \sqrt{324 - 4 \cdot 81}}{2 \cdot 1}$

Multiply $- 4$ by $81$ .

$x = \frac{18 \pm \sqrt{324 - 324}}{2 \cdot 1}$

Subtract $324$ from $324$ .

$x = \frac{18 \pm \sqrt{0}}{2 \cdot 1}$

Rewrite $0$ as $0^{2}$ .

$x = \frac{18 \pm \sqrt{0^{2}}}{2 \cdot 1}$

Pull terms out from under the radical, assuming positive real numbers.

$x = \frac{18 \pm 0}{2 \cdot 1}$

$18$ plus or minus $0$ is $18$ .

$x = \frac{18}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{18}{2}$

Divide $18$ by $2$ .

$x = 9$

Step 5

The final answer is the combination of both solutions.

$x = 9$ Double roots

Solve Using the Quadratic Formula (x-8)(x-10)=-1

Related Questions

Support LCMGCF.com by disabling your adblocker.