Solve Using the Quadratic Formula (x-1)^2-20=44

${(x - 1)}^{2} - 20 = 44$

Step 1

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

Subtract $44$ from both sides of the equation.

${(x - 1)}^{2} - 20 - 44 = 0$

Simplify ${(x - 1)}^{2} - 20 - 44$ .

Simplify each term.

Rewrite ${(x - 1)}^{2}$ as $(x - 1) (x - 1)$ .

$(x - 1) (x - 1) - 20 - 44 = 0$

Expand $(x - 1) (x - 1)$ using the FOIL Method.

Apply the distributive property.

$x (x - 1) - 1 (x - 1) - 20 - 44 = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 1 - 1 (x - 1) - 20 - 44 = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 1 - 1 x - 1 \cdot - 1 - 20 - 44 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 1 - 1 x - 1 \cdot - 1 - 20 - 44 = 0$

Move $- 1$ to the left of $x$ .

$x^{2} - 1 \cdot x - 1 x - 1 \cdot - 1 - 20 - 44 = 0$

Rewrite $- 1 x$ as $- x$ .

$x^{2} - x - 1 x - 1 \cdot - 1 - 20 - 44 = 0$

Rewrite $- 1 x$ as $- x$ .

$x^{2} - x - x - 1 \cdot - 1 - 20 - 44 = 0$

Multiply $- 1$ by $- 1$ .

$x^{2} - x - x + 1 - 20 - 44 = 0$

Subtract $x$ from $- x$ .

$x^{2} - 2 x + 1 - 20 - 44 = 0$

Subtract $20$ from $1$ .

$x^{2} - 2 x - 19 - 44 = 0$

Subtract $44$ from $- 19$ .

$x^{2} - 2 x - 63 = 0$

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 $a = 1$ , $b = - 2$ , and $c = - 63$ into the quadratic formula and solve for $x$ .

$\frac{2 \pm \sqrt{{(- 2)}^{2} - 4 \cdot (1 \cdot - 63)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{2 \pm \sqrt{4 - 4 \cdot 1 \cdot - 63}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 63$ .

Multiply $- 4$ by $1$ .

$x = \frac{2 \pm \sqrt{4 - 4 \cdot - 63}}{2 \cdot 1}$

Multiply $- 4$ by $- 63$ .

$x = \frac{2 \pm \sqrt{4 + 252}}{2 \cdot 1}$

Add $4$ and $252$ .

$x = \frac{2 \pm \sqrt{256}}{2 \cdot 1}$

Rewrite $256$ as $16^{2}$ .

$x = \frac{2 \pm \sqrt{16^{2}}}{2 \cdot 1}$

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

$x = \frac{2 \pm 16}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{2 \pm 16}{2}$

Simplify $\frac{2 \pm 16}{2}$ .

$x = 1 \pm 8$

Step 5

The final answer is the combination of both solutions.

$x = 9, - 7$

Solve Using the Quadratic Formula (x-1)^2-20=44

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