Solve by Completing the Square (x^2)/6-x=12

$\frac{x^{2}}{6} - x = 12$

Step 1

Multiply each term in $\frac{x^{2}}{6} - x = 12$ by $6$ to eliminate the fractions.

Multiply each term in $\frac{x^{2}}{6} - x = 12$ by $6$ .

$\frac{x^{2}}{6} \cdot 6 - x \cdot 6 = 12 \cdot 6$

Simplify the left side.

Simplify each term.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{x^{2}}{6} \cdot 6 - x \cdot 6 = 12 \cdot 6$

Rewrite the expression.

$x^{2} - x \cdot 6 = 12 \cdot 6$

Multiply $6$ by $- 1$ .

$x^{2} - 6 x = 12 \cdot 6$

Simplify the right side.

Multiply $12$ by $6$ .

$x^{2} - 6 x = 72$

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 $b$ .

${(\frac{b}{2})}^{2} = {(- 3)}^{2}$

Step 3

Add the term to each side of the equation.

$x^{2} - 6 x + {(- 3)}^{2} = 72 + {(- 3)}^{2}$

Step 4

Simplify the equation.

Simplify the left side.

Raise $- 3$ to the power of $2$ .

$x^{2} - 6 x + 9 = 72 + {(- 3)}^{2}$

Simplify the right side.

Simplify $72 + {(- 3)}^{2}$ .

Raise $- 3$ to the power of $2$ .

$x^{2} - 6 x + 9 = 72 + 9$

Add $72$ and $9$ .

$x^{2} - 6 x + 9 = 81$

Step 5

Factor the perfect trinomial square into ${(x - 3)}^{2}$ .

${(x - 3)}^{2} = 81$

Step 6

Solve the equation for $x$ .

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

$x - 3 = \pm \sqrt{81}$

Simplify $\pm \sqrt{81}$ .

Rewrite $81$ as $9^{2}$ .

$x - 3 = \pm \sqrt{9^{2}}$

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

$x - 3 = \pm 9$

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

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

$x - 3 = 9$

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

Add $3$ to both sides of the equation.

$x = 9 + 3$

Add $9$ and $3$ .

$x = 12$

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

$x - 3 = - 9$

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

Add $3$ to both sides of the equation.

$x = - 9 + 3$

Add $- 9$ and $3$ .

$x = - 6$

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

$x = 12, - 6$

Solve by Completing the Square (x^2)/6-x=12

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