Algebra Examples

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

Step 1

Simplify the left side.

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Step 1.1

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

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Step 1.1.1

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

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Step 1.1.1.1

Apply the distributive property.

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

Step 1.1.1.2

Apply the distributive property.

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

Step 1.1.1.3

Apply the distributive property.

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

Step 1.1.2

Simplify and combine like terms.

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Step 1.1.2.1

Simplify each term.

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Step 1.1.2.1.1

Multiply $x$ by $x$ .

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

Step 1.1.2.1.2

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

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

Step 1.1.2.1.3

Multiply $- 5$ by $- 5$ .

$x^{2} - 5 x - 5 x + 25 = 0$

Step 1.1.2.2

Subtract $5 x$ from $- 5 x$ .

$x^{2} - 10 x + 25 = 0$

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 $a = 1$ , $b = - 10$ , and $c = 25$ into the quadratic formula and solve for $x$ .

$\frac{10 \pm \sqrt{{(- 10)}^{2} - 4 \cdot (1 \cdot 25)}}{2 \cdot 1}$

Step 4

Simplify.

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Raise $- 10$ to the power of $2$ .

$x = \frac{10 \pm \sqrt{100 - 4 \cdot 1 \cdot 25}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot 25$ .

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Step 4.1.2.1

Multiply $- 4$ by $1$ .

$x = \frac{10 \pm \sqrt{100 - 4 \cdot 25}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $25$ .

$x = \frac{10 \pm \sqrt{100 - 100}}{2 \cdot 1}$

Step 4.1.3

Subtract $100$ from $100$ .

$x = \frac{10 \pm \sqrt{0}}{2 \cdot 1}$

Step 4.1.4

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

$x = \frac{10 \pm \sqrt{0^{2}}}{2 \cdot 1}$

Step 4.1.5

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

$x = \frac{10 \pm 0}{2 \cdot 1}$

Step 4.1.6

$10$ plus or minus $0$ is $10$ .

$x = \frac{10}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$x = \frac{10}{2}$

Step 4.3

Divide $10$ by $2$ .

$x = 5$

Step 5

The final answer is the combination of both solutions.

$x = 5$ Double roots