Algebra Examples

$(x - 12) (x + 4) = 9$

Step 1

Simplify the equation into a proper form to complete the square.

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Step 1.1

Simplify $(x - 12) (x + 4)$ .

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Step 1.1.1

Expand $(x - 12) (x + 4)$ using the FOIL Method.

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Step 1.1.1.1

Apply the distributive property.

$x (x + 4) - 12 (x + 4) = 9$

Step 1.1.1.2

Apply the distributive property.

$x \cdot x + x \cdot 4 - 12 (x + 4) = 9$

Step 1.1.1.3

Apply the distributive property.

$x \cdot x + x \cdot 4 - 12 x - 12 \cdot 4 = 9$

Step 1.1.2

Simplify and combine like terms.

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Step 1.1.2.1

Simplify each term.

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Step 1.1.2.1.1

Multiply $x$ by $x$ .

$x^{2} + x \cdot 4 - 12 x - 12 \cdot 4 = 9$

Step 1.1.2.1.2

Move $4$ to the left of $x$ .

$x^{2} + 4 \cdot x - 12 x - 12 \cdot 4 = 9$

Step 1.1.2.1.3

Multiply $- 12$ by $4$ .

$x^{2} + 4 x - 12 x - 48 = 9$

Step 1.1.2.2

Subtract $12 x$ from $4 x$ .

$x^{2} - 8 x - 48 = 9$

Step 1.2

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

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Step 1.2.1

Add $48$ to both sides of the equation.

$x^{2} - 8 x = 9 + 48$

Step 1.2.2

Add $9$ and $48$ .

$x^{2} - 8 x = 57$

Step 2

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of $b$ .

${(\frac{b}{2})}^{2} = {(- 4)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} - 8 x + {(- 4)}^{2} = 57 + {(- 4)}^{2}$

Step 4

Simplify the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Raise $- 4$ to the power of $2$ .

$x^{2} - 8 x + 16 = 57 + {(- 4)}^{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $57 + {(- 4)}^{2}$ .

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Step 4.2.1.1

Raise $- 4$ to the power of $2$ .

$x^{2} - 8 x + 16 = 57 + 16$

Step 4.2.1.2

Add $57$ and $16$ .

$x^{2} - 8 x + 16 = 73$

Step 5

Factor the perfect trinomial square into ${(x - 4)}^{2}$ .

${(x - 4)}^{2} = 73$

Step 6

Solve the equation for $x$ .

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Step 6.1

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

$x - 4 = \pm \sqrt{73}$

Step 6.2

Add $4$ to both sides of the equation.

$x = \pm \sqrt{73} + 4$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm \sqrt{73} + 4$

Decimal Form:

$x = 12.54400374 \dots, - 4.54400374 \dots$