Solve Using the Quadratic Formula (x-4)(x-4)=0

$(x - 4) (x - 4) = 0$

Step 1

Simplify the left side.

Simplify $(x - 4) (x - 4)$ .

Expand $(x - 4) (x - 4)$ using the FOIL Method.

Apply the distributive property.

$x (x - 4) - 4 (x - 4) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 4 - 4 (x - 4) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 4 - 4 x - 4 \cdot - 4 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 4 - 4 x - 4 \cdot - 4 = 0$

Move $- 4$ to the left of $x$ .

$x^{2} - 4 \cdot x - 4 x - 4 \cdot - 4 = 0$

Multiply $- 4$ by $- 4$ .

$x^{2} - 4 x - 4 x + 16 = 0$

Subtract $4 x$ from $- 4 x$ .

$x^{2} - 8 x + 16 = 0$

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 $a = 1$ , $b = - 8$ , and $c = 16$ into the quadratic formula and solve for $x$ .

$\frac{8 \pm \sqrt{{(- 8)}^{2} - 4 \cdot (1 \cdot 16)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 8$ to the power of $2$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 1 \cdot 16}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot 16$ .

Multiply $- 4$ by $1$ .

$x = \frac{8 \pm \sqrt{64 - 4 \cdot 16}}{2 \cdot 1}$

Multiply $- 4$ by $16$ .

$x = \frac{8 \pm \sqrt{64 - 64}}{2 \cdot 1}$

Subtract $64$ from $64$ .

$x = \frac{8 \pm \sqrt{0}}{2 \cdot 1}$

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

$x = \frac{8 \pm \sqrt{0^{2}}}{2 \cdot 1}$

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

$x = \frac{8 \pm 0}{2 \cdot 1}$

$8$ plus or minus $0$ is $8$ .

$x = \frac{8}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{8}{2}$

Divide $8$ by $2$ .

$x = 4$

Step 5

The final answer is the combination of both solutions.

$x = 4$ Double roots

Solve Using the Quadratic Formula (x-4)(x-4)=0

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