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

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

Step 1

Simplify the left side.

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify terms.

Combine the opposite terms in $x \cdot x + x \cdot - 5 + 5 x + 5 \cdot - 5$ .

Reorder the factors in the terms $x \cdot - 5$ and $5 x$ .

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

Add $- 5 x$ and $5 x$ .

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

Add $x \cdot x$ and $0$ .

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

Simplify each term.

Multiply $x$ by $x$ .

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

Multiply $5$ by $- 5$ .

$x^{2} - 25 = 0$

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 $a = 1$ , $b = 0$ , and $c = - 25$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot - 25)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raising $0$ to any positive power yields $0$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 25}}{2 \cdot 1}$

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

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 25}}{2 \cdot 1}$

Multiply $- 4$ by $- 25$ .

$x = \frac{0 \pm \sqrt{0 + 100}}{2 \cdot 1}$

Add $0$ and $100$ .

$x = \frac{0 \pm \sqrt{100}}{2 \cdot 1}$

Rewrite $100$ as $10^{2}$ .

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

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

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

Multiply $2$ by $1$ .

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

Simplify $\frac{0 \pm 10}{2}$ .

$x = \pm 5$

Step 5

The final answer is the combination of both solutions.

$x = 5, - 5$

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

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