Solve Using the Quadratic Formula (x-1)(x-5)=0

$(x - 1) (x - 5) = 0$

Step 1

Simplify the left side.

Simplify $(x - 1) (x - 5)$ .

Expand $(x - 1) (x - 5)$ using the FOIL Method.

Apply the distributive property.

$x (x - 5) - 1 (x - 5) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 5 - 1 (x - 5) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 5 - 1 x - 1 \cdot - 5 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 5 - 1 x - 1 \cdot - 5 = 0$

Move $- 5$ to the left of $x$ .

$x^{2} - 5 \cdot x - 1 x - 1 \cdot - 5 = 0$

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

$x^{2} - 5 x - x - 1 \cdot - 5 = 0$

Multiply $- 1$ by $- 5$ .

$x^{2} - 5 x - x + 5 = 0$

Subtract $x$ from $- 5 x$ .

$x^{2} - 6 x + 5 = 0$

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 $a = 1$ , $b = - 6$ , and $c = 5$ into the quadratic formula and solve for $x$ .

$\frac{6 \pm \sqrt{{(- 6)}^{2} - 4 \cdot (1 \cdot 5)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 6$ to the power of $2$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot 1 \cdot 5}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 5$ .

Multiply $- 4$ by $1$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot 5}}{2 \cdot 1}$

Multiply $- 4$ by $5$ .

$x = \frac{6 \pm \sqrt{36 - 20}}{2 \cdot 1}$

Subtract $20$ from $36$ .

$x = \frac{6 \pm \sqrt{16}}{2 \cdot 1}$

Rewrite $16$ as $4^{2}$ .

$x = \frac{6 \pm \sqrt{4^{2}}}{2 \cdot 1}$

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

$x = \frac{6 \pm 4}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{6 \pm 4}{2}$

Simplify $\frac{6 \pm 4}{2}$ .

$x = 3 \pm 2$

Step 5

The final answer is the combination of both solutions.

$x = 5, 1$

Solve Using the Quadratic Formula (x-1)(x-5)=0

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