Algebra Examples

$x^{2} - 14 x - 284 = - 2 x$

Step 1

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

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Step 1.1

Add $284$ to both sides of the equation.

$x^{2} - 14 x = - 2 x + 284$

Step 1.2

Move all terms containing $x$ to the left side of the equation.

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Step 1.2.1

Add $2 x$ to both sides of the equation.

$x^{2} - 14 x + 2 x = 284$

Step 1.2.2

Add $- 14 x$ and $2 x$ .

$x^{2} - 12 x = 284$

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 $b$ .

${(\frac{b}{2})}^{2} = {(- 6)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} - 12 x + {(- 6)}^{2} = 284 + {(- 6)}^{2}$

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 $- 6$ to the power of $2$ .

$x^{2} - 12 x + 36 = 284 + {(- 6)}^{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $284 + {(- 6)}^{2}$ .

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Step 4.2.1.1

Raise $- 6$ to the power of $2$ .

$x^{2} - 12 x + 36 = 284 + 36$

Step 4.2.1.2

Add $284$ and $36$ .

$x^{2} - 12 x + 36 = 320$

Step 5

Factor the perfect trinomial square into ${(x - 6)}^{2}$ .

${(x - 6)}^{2} = 320$

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.

$x - 6 = \pm \sqrt{320}$

Step 6.2

Simplify $\pm \sqrt{320}$ .

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Step 6.2.1

Rewrite $320$ as $8^{2} \cdot 5$ .

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Step 6.2.1.1

Factor $64$ out of $320$ .

$x - 6 = \pm \sqrt{64 (5)}$

Step 6.2.1.2

Rewrite $64$ as $8^{2}$ .

$x - 6 = \pm \sqrt{8^{2} \cdot 5}$

Step 6.2.2

Pull terms out from under the radical.

$x - 6 = \pm 8 \sqrt{5}$

Step 6.3

Add $6$ to both sides of the equation.

$x = \pm 8 \sqrt{5} + 6$

Step 7

The result can be shown in multiple forms.

Exact Form:

$x = \pm 8 \sqrt{5} + 6$

Decimal Form:

$x = 23.88854381 \dots, - 11.88854381 \dots$