Solve Using the Quadratic Formula (x+7)(x-7)=0

$(x + 7) (x - 7) = 0$

Step 1

Simplify the left side.

Simplify $(x + 7) (x - 7)$ .

Expand $(x + 7) (x - 7)$ using the FOIL Method.

Apply the distributive property.

$x (x - 7) + 7 (x - 7) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 7 + 7 (x - 7) = 0$

Apply the distributive property.

$x \cdot x + x \cdot - 7 + 7 x + 7 \cdot - 7 = 0$

Simplify terms.

Combine the opposite terms in $x \cdot x + x \cdot - 7 + 7 x + 7 \cdot - 7$ .

Reorder the factors in the terms $x \cdot - 7$ and $7 x$ .

$x \cdot x - 7 x + 7 x + 7 \cdot - 7 = 0$

Add $- 7 x$ and $7 x$ .

$x \cdot x + 0 + 7 \cdot - 7 = 0$

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

$x \cdot x + 7 \cdot - 7 = 0$

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + 7 \cdot - 7 = 0$

Multiply $7$ by $- 7$ .

$x^{2} - 49 = 0$

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 $c = - 49$ into the quadratic formula and solve for $x$ .

$\frac{0 \pm \sqrt{0^{2} - 4 \cdot (1 \cdot - 49)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

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

$x = \frac{0 \pm \sqrt{0 - 4 \cdot 1 \cdot - 49}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 49$ .

Multiply $- 4$ by $1$ .

$x = \frac{0 \pm \sqrt{0 - 4 \cdot - 49}}{2 \cdot 1}$

Multiply $- 4$ by $- 49$ .

$x = \frac{0 \pm \sqrt{0 + 196}}{2 \cdot 1}$

Add $0$ and $196$ .

$x = \frac{0 \pm \sqrt{196}}{2 \cdot 1}$

Rewrite $196$ as $14^{2}$ .

$x = \frac{0 \pm \sqrt{14^{2}}}{2 \cdot 1}$

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

$x = \frac{0 \pm 14}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{0 \pm 14}{2}$

Simplify $\frac{0 \pm 14}{2}$ .

$x = \pm 7$

Step 5

The final answer is the combination of both solutions.

$x = 7, - 7$

Solve Using the Quadratic Formula (x+7)(x-7)=0

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