Pre-Algebra Examples

${(x + 6)}^{2} = 13$

Step 1

Simplify ${(x + 6)}^{2}$ .

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Step 1.1

Rewrite ${(x + 6)}^{2}$ as $(x + 6) (x + 6)$ .

$(x + 6) (x + 6) = 13$

Step 1.2

Expand $(x + 6) (x + 6)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$x (x + 6) + 6 (x + 6) = 13$

Step 1.2.2

Apply the distributive property.

$x \cdot x + x \cdot 6 + 6 (x + 6) = 13$

Step 1.2.3

Apply the distributive property.

$x \cdot x + x \cdot 6 + 6 x + 6 \cdot 6 = 13$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 6 + 6 x + 6 \cdot 6 = 13$

Step 1.3.1.2

Move $6$ to the left of $x$ .

$x^{2} + 6 \cdot x + 6 x + 6 \cdot 6 = 13$

Step 1.3.1.3

Multiply $6$ by $6$ .

$x^{2} + 6 x + 6 x + 36 = 13$

Step 1.3.2

Add $6 x$ and $6 x$ .

$x^{2} + 12 x + 36 = 13$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x \approx - 9.60555127, - 2.39444872$

Step 3