Pre-Algebra Examples

$(x + 3) (x - 3) - 40 = 0$

Step 1

Simplify $(x + 3) (x - 3) - 40$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

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

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Step 1.1.1.1

Apply the distributive property.

$x (x - 3) + 3 (x - 3) - 40 = 0$

Step 1.1.1.2

Apply the distributive property.

$x \cdot x + x \cdot - 3 + 3 (x - 3) - 40 = 0$

Step 1.1.1.3

Apply the distributive property.

$x \cdot x + x \cdot - 3 + 3 x + 3 \cdot - 3 - 40 = 0$

Step 1.1.2

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

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Step 1.1.2.1

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

$x \cdot x - 3 x + 3 x + 3 \cdot - 3 - 40 = 0$

Step 1.1.2.2

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

$x \cdot x + 0 + 3 \cdot - 3 - 40 = 0$

Step 1.1.2.3

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

$x \cdot x + 3 \cdot - 3 - 40 = 0$

Step 1.1.3

Simplify each term.

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Step 1.1.3.1

Multiply $x$ by $x$ .

$x^{2} + 3 \cdot - 3 - 40 = 0$

Step 1.1.3.2

Multiply $3$ by $- 3$ .

$x^{2} - 9 - 40 = 0$

Step 1.2

Subtract $40$ from $- 9$ .

$x^{2} - 49 = 0$

Step 2

Add $49$ to both sides of the equation.

$x^{2} = 49$

Step 3

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

$x = \pm \sqrt{49}$

Step 4

Simplify $\pm \sqrt{49}$ .

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Step 4.1

Rewrite $49$ as $7^{2}$ .

$x = \pm \sqrt{7^{2}}$

Step 4.2

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

$x = \pm 7$

Step 5

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

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Step 5.1

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

$x = 7$

Step 5.2

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

$x = - 7$

Step 5.3

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

$x = 7, - 7$