Pre-Algebra Examples

$\frac{m^{2}}{6} = m + \frac{5}{6}$

Step 1

Multiply both sides by $6$ .

$\frac{m^{2}}{6} \cdot 6 = (m + \frac{5}{6}) \cdot 6$

Step 2

Simplify.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

Cancel the common factor of $6$ .

Tap for more steps...

Step 2.1.1.1

Cancel the common factor.

$\frac{m^{2}}{6} \cdot 6 = (m + \frac{5}{6}) \cdot 6$

Step 2.1.1.2

Rewrite the expression.

$m^{2} = (m + \frac{5}{6}) \cdot 6$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

Simplify $(m + \frac{5}{6}) \cdot 6$ .

Tap for more steps...

Step 2.2.1.1

Apply the distributive property.

$m^{2} = m \cdot 6 + \frac{5}{6} \cdot 6$

Step 2.2.1.2

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

$m^{2} = 6 \cdot m + \frac{5}{6} \cdot 6$

Step 2.2.1.3

Cancel the common factor of $6$ .

Tap for more steps...

Step 2.2.1.3.1

Cancel the common factor.

$m^{2} = 6 \cdot m + \frac{5}{6} \cdot 6$

Step 2.2.1.3.2

Rewrite the expression.

$m^{2} = 6 \cdot m + 5$

$m^{2} = 6 m + 5$

Step 3

Solve for $m$ .

Tap for more steps...

Step 3.1

Subtract $6 m$ from both sides of the equation.

$m^{2} - 6 m = 5$

Step 3.2

Subtract $5$ from both sides of the equation.

$m^{2} - 6 m - 5 = 0$

Step 3.3

Use the quadratic formula to find the solutions.

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

Step 3.4

Substitute the values $a = 1$ , $b = - 6$ , and $c = - 5$ into the quadratic formula and solve for $m$ .

$\frac{6 \pm \sqrt{{(- 6)}^{2} - 4 \cdot (1 \cdot - 5)}}{2 \cdot 1}$

Step 3.5

Simplify.

Tap for more steps...

Step 3.5.1

Simplify the numerator.

Tap for more steps...

Step 3.5.1.1

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

$m = \frac{6 \pm \sqrt{36 - 4 \cdot 1 \cdot - 5}}{2 \cdot 1}$

Step 3.5.1.2

Multiply $- 4 \cdot 1 \cdot - 5$ .

Tap for more steps...

Step 3.5.1.2.1

Multiply $- 4$ by $1$ .

$m = \frac{6 \pm \sqrt{36 - 4 \cdot - 5}}{2 \cdot 1}$

Step 3.5.1.2.2

Multiply $- 4$ by $- 5$ .

$m = \frac{6 \pm \sqrt{36 + 20}}{2 \cdot 1}$

Step 3.5.1.3

Add $36$ and $20$ .

$m = \frac{6 \pm \sqrt{56}}{2 \cdot 1}$

Step 3.5.1.4

Rewrite $56$ as $2^{2} \cdot 14$ .

Tap for more steps...

Step 3.5.1.4.1

Factor $4$ out of $56$ .

$m = \frac{6 \pm \sqrt{4 (14)}}{2 \cdot 1}$

Step 3.5.1.4.2

Rewrite $4$ as $2^{2}$ .

$m = \frac{6 \pm \sqrt{2^{2} \cdot 14}}{2 \cdot 1}$

Step 3.5.1.5

Pull terms out from under the radical.

$m = \frac{6 \pm 2 \sqrt{14}}{2 \cdot 1}$

Step 3.5.2

Multiply $2$ by $1$ .

$m = \frac{6 \pm 2 \sqrt{14}}{2}$

Step 3.5.3

Simplify $\frac{6 \pm 2 \sqrt{14}}{2}$ .

$m = 3 \pm \sqrt{14}$

Step 3.6

Simplify the expression to solve for the $+$ portion of the $\pm$ .

Tap for more steps...

Step 3.6.1

Simplify the numerator.

Tap for more steps...

Step 3.6.1.1

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

$m = \frac{6 \pm \sqrt{36 - 4 \cdot 1 \cdot - 5}}{2 \cdot 1}$

Step 3.6.1.2

Multiply $- 4 \cdot 1 \cdot - 5$ .

Tap for more steps...

Step 3.6.1.2.1

Multiply $- 4$ by $1$ .

$m = \frac{6 \pm \sqrt{36 - 4 \cdot - 5}}{2 \cdot 1}$

Step 3.6.1.2.2

Multiply $- 4$ by $- 5$ .

$m = \frac{6 \pm \sqrt{36 + 20}}{2 \cdot 1}$

Step 3.6.1.3

Add $36$ and $20$ .

$m = \frac{6 \pm \sqrt{56}}{2 \cdot 1}$

Step 3.6.1.4

Rewrite $56$ as $2^{2} \cdot 14$ .

Tap for more steps...

Step 3.6.1.4.1

Factor $4$ out of $56$ .

$m = \frac{6 \pm \sqrt{4 (14)}}{2 \cdot 1}$

Step 3.6.1.4.2

Rewrite $4$ as $2^{2}$ .

$m = \frac{6 \pm \sqrt{2^{2} \cdot 14}}{2 \cdot 1}$

Step 3.6.1.5

Pull terms out from under the radical.

$m = \frac{6 \pm 2 \sqrt{14}}{2 \cdot 1}$

Step 3.6.2

Multiply $2$ by $1$ .

$m = \frac{6 \pm 2 \sqrt{14}}{2}$

Step 3.6.3

Simplify $\frac{6 \pm 2 \sqrt{14}}{2}$ .

$m = 3 \pm \sqrt{14}$

Step 3.6.4

Change the $\pm$ to $+$ .

$m = 3 + \sqrt{14}$

Step 3.7

Simplify the expression to solve for the $-$ portion of the $\pm$ .

Tap for more steps...

Step 3.7.1

Simplify the numerator.

Tap for more steps...

Step 3.7.1.1

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

$m = \frac{6 \pm \sqrt{36 - 4 \cdot 1 \cdot - 5}}{2 \cdot 1}$

Step 3.7.1.2

Multiply $- 4 \cdot 1 \cdot - 5$ .

Tap for more steps...

Step 3.7.1.2.1

Multiply $- 4$ by $1$ .

$m = \frac{6 \pm \sqrt{36 - 4 \cdot - 5}}{2 \cdot 1}$

Step 3.7.1.2.2

Multiply $- 4$ by $- 5$ .

$m = \frac{6 \pm \sqrt{36 + 20}}{2 \cdot 1}$

Step 3.7.1.3

Add $36$ and $20$ .

$m = \frac{6 \pm \sqrt{56}}{2 \cdot 1}$

Step 3.7.1.4

Rewrite $56$ as $2^{2} \cdot 14$ .

Tap for more steps...

Step 3.7.1.4.1

Factor $4$ out of $56$ .

$m = \frac{6 \pm \sqrt{4 (14)}}{2 \cdot 1}$

Step 3.7.1.4.2

Rewrite $4$ as $2^{2}$ .

$m = \frac{6 \pm \sqrt{2^{2} \cdot 14}}{2 \cdot 1}$

Step 3.7.1.5

Pull terms out from under the radical.

$m = \frac{6 \pm 2 \sqrt{14}}{2 \cdot 1}$

Step 3.7.2

Multiply $2$ by $1$ .

$m = \frac{6 \pm 2 \sqrt{14}}{2}$

Step 3.7.3

Simplify $\frac{6 \pm 2 \sqrt{14}}{2}$ .

$m = 3 \pm \sqrt{14}$

Step 3.7.4

Change the $\pm$ to $-$ .

$m = 3 - \sqrt{14}$

Step 3.8

The final answer is the combination of both solutions.

$m = 3 + \sqrt{14}, 3 - \sqrt{14}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$m = 3 + \sqrt{14}, 3 - \sqrt{14}$

Decimal Form:

$m = 6.74165738 \dots, - 0.74165738 \dots$