Pre-Algebra Examples

$(x - 5) (x + 5) = 11$

Step 1

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

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Apply the distributive property.

$x (x + 5) - 5 (x + 5) = 11$

Step 1.1.2

Apply the distributive property.

$x \cdot x + x \cdot 5 - 5 (x + 5) = 11$

Step 1.1.3

Apply the distributive property.

$x \cdot x + x \cdot 5 - 5 x - 5 \cdot 5 = 11$

Step 1.2

Simplify terms.

Tap for more steps...

Step 1.2.1

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

Tap for more steps...

Step 1.2.1.1

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

$x \cdot x + 5 x - 5 x - 5 \cdot 5 = 11$

Step 1.2.1.2

Subtract $5 x$ from $5 x$ .

$x \cdot x + 0 - 5 \cdot 5 = 11$

Step 1.2.1.3

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

$x \cdot x - 5 \cdot 5 = 11$

Step 1.2.2

Simplify each term.

Tap for more steps...

Step 1.2.2.1

Multiply $x$ by $x$ .

$x^{2} - 5 \cdot 5 = 11$

Step 1.2.2.2

Multiply $- 5$ by $5$ .

$x^{2} - 25 = 11$

Step 2

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

Tap for more steps...

Step 2.1

Add $25$ to both sides of the equation.

$x^{2} = 11 + 25$

Step 2.2

Add $11$ and $25$ .

$x^{2} = 36$

Step 3

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

$x = \pm \sqrt{36}$

Step 4

Simplify $\pm \sqrt{36}$ .

Tap for more steps...

Step 4.1

Rewrite $36$ as $6^{2}$ .

$x = \pm \sqrt{6^{2}}$

Step 4.2

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

$x = \pm 6$

Step 5

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

Tap for more steps...

Step 5.1

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

$x = 6$

Step 5.2

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

$x = - 6$

Step 5.3

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

$x = 6, - 6$