Solve for x (x+3)(x-3)=7

$(x + 3) (x - 3) = 7$

Step 1

Simplify $(x + 3) (x - 3)$ .

Expand $(x + 3) (x - 3)$ using the FOIL Method.

Apply the distributive property.

$x (x - 3) + 3 (x - 3) = 7$

Apply the distributive property.

$x \cdot x + x \cdot - 3 + 3 (x - 3) = 7$

Apply the distributive property.

$x \cdot x + x \cdot - 3 + 3 x + 3 \cdot - 3 = 7$

Simplify terms.

Combine the opposite terms in $x \cdot x + x \cdot - 3 + 3 x + 3 \cdot - 3$ .

Reorder the factors in the terms $x \cdot - 3$ and $3 x$ .

$x \cdot x - 3 x + 3 x + 3 \cdot - 3 = 7$

Add $- 3 x$ and $3 x$ .

$x \cdot x + 0 + 3 \cdot - 3 = 7$

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

$x \cdot x + 3 \cdot - 3 = 7$

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + 3 \cdot - 3 = 7$

Multiply $3$ by $- 3$ .

$x^{2} - 9 = 7$

Step 2

Move all terms not containing $x$ to the right side of the equation.

Add $9$ to both sides of the equation.

$x^{2} = 7 + 9$

Add $7$ and $9$ .

$x^{2} = 16$

Step 3

Take the square root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{16}$

Step 4

Simplify $\pm \sqrt{16}$ .

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

$x = \pm \sqrt{4^{2}}$

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

$x = \pm 4$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = 4$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - 4$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 4, - 4$

Solve for x (x+3)(x-3)=7

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