Solve Using the Quadratic Formula (x^2)/6-x=12

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

Step 1

Subtract $12$ from both sides of the equation.

$\frac{x^{2}}{6} - x - 12 = 0$

Step 2

Multiply through by the least common denominator $6$ , then simplify.

Apply the distributive property.

$6 (\frac{x^{2}}{6}) + 6 (- x) + 6 \cdot - 12 = 0$

Simplify.

Cancel the common factor of $6$ .

Cancel the common factor.

$6 (\frac{x^{2}}{6}) + 6 (- x) + 6 \cdot - 12 = 0$

Rewrite the expression.

$x^{2} + 6 (- x) + 6 \cdot - 12 = 0$

Multiply $- 1$ by $6$ .

$x^{2} - 6 x + 6 \cdot - 12 = 0$

Multiply $6$ by $- 12$ .

$x^{2} - 6 x - 72 = 0$

Step 3

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 4

Substitute the values $a = 1$ , $b = - 6$ , and $c = - 72$ into the quadratic formula and solve for $x$ .

$\frac{6 \pm \sqrt{{(- 6)}^{2} - 4 \cdot (1 \cdot - 72)}}{2 \cdot 1}$

Step 5

Simplify.

Simplify the numerator.

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

$x = \frac{6 \pm \sqrt{36 - 4 \cdot 1 \cdot - 72}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 72$ .

Multiply $- 4$ by $1$ .

$x = \frac{6 \pm \sqrt{36 - 4 \cdot - 72}}{2 \cdot 1}$

Multiply $- 4$ by $- 72$ .

$x = \frac{6 \pm \sqrt{36 + 288}}{2 \cdot 1}$

Add $36$ and $288$ .

$x = \frac{6 \pm \sqrt{324}}{2 \cdot 1}$

Rewrite $324$ as $18^{2}$ .

$x = \frac{6 \pm \sqrt{18^{2}}}{2 \cdot 1}$

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

$x = \frac{6 \pm 18}{2 \cdot 1}$

Multiply $2$ by $1$ .

$x = \frac{6 \pm 18}{2}$

Simplify $\frac{6 \pm 18}{2}$ .

$x = 3 \pm 9$

Step 6

The final answer is the combination of both solutions.

$x = 12, - 6$

Solve Using the Quadratic Formula (x^2)/6-x=12

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