Basic Math Examples

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

Step 1

Since $m$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

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

Step 2

Simplify $2 m (m + 4)$ .

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Step 2.1

Rewrite.

$0 + 0 + 2 m (m + 4) = m^{2} - 8$

Step 2.2

Simplify by adding zeros.

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

Step 2.3

Apply the distributive property.

$2 m \cdot m + 2 m \cdot 4 = m^{2} - 8$

Step 2.4

Multiply $m$ by $m$ by adding the exponents.

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Step 2.4.1

Move $m$ .

$2 (m \cdot m) + 2 m \cdot 4 = m^{2} - 8$

Step 2.4.2

Multiply $m$ by $m$ .

$2 m^{2} + 2 m \cdot 4 = m^{2} - 8$

Step 2.5

Multiply $4$ by $2$ .

$2 m^{2} + 8 m = m^{2} - 8$

Step 3

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

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Step 3.1

Subtract $m^{2}$ from both sides of the equation.

$2 m^{2} + 8 m - m^{2} = - 8$

Step 3.2

Subtract $m^{2}$ from $2 m^{2}$ .

$m^{2} + 8 m = - 8$

Step 4

Add $8$ to both sides of the equation.

$m^{2} + 8 m + 8 = 0$

Step 5

Use the quadratic formula to find the solutions.

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

Step 6

Substitute the values $a = 1$ , $b = 8$ , and $c = 8$ into the quadratic formula and solve for $m$ .

$\frac{- 8 \pm \sqrt{8^{2} - 4 \cdot (1 \cdot 8)}}{2 \cdot 1}$

Step 7

Simplify.

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Step 7.1

Simplify the numerator.

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Step 7.1.1

Raise $8$ to the power of $2$ .

$m = \frac{- 8 \pm \sqrt{64 - 4 \cdot 1 \cdot 8}}{2 \cdot 1}$

Step 7.1.2

Multiply $- 4 \cdot 1 \cdot 8$ .

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Step 7.1.2.1

Multiply $- 4$ by $1$ .

$m = \frac{- 8 \pm \sqrt{64 - 4 \cdot 8}}{2 \cdot 1}$

Step 7.1.2.2

Multiply $- 4$ by $8$ .

$m = \frac{- 8 \pm \sqrt{64 - 32}}{2 \cdot 1}$

Step 7.1.3

Subtract $32$ from $64$ .

$m = \frac{- 8 \pm \sqrt{32}}{2 \cdot 1}$

Step 7.1.4

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 7.1.4.1

Factor $16$ out of $32$ .

$m = \frac{- 8 \pm \sqrt{16 (2)}}{2 \cdot 1}$

Step 7.1.4.2

Rewrite $16$ as $4^{2}$ .

$m = \frac{- 8 \pm \sqrt{4^{2} \cdot 2}}{2 \cdot 1}$

Step 7.1.5

Pull terms out from under the radical.

$m = \frac{- 8 \pm 4 \sqrt{2}}{2 \cdot 1}$

Step 7.2

Multiply $2$ by $1$ .

$m = \frac{- 8 \pm 4 \sqrt{2}}{2}$

Step 7.3

Simplify $\frac{- 8 \pm 4 \sqrt{2}}{2}$ .

$m = - 4 \pm 2 \sqrt{2}$

Step 8

The final answer is the combination of both solutions.

$m = - 4 + 2 \sqrt{2}, - 4 - 2 \sqrt{2}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$m = - 4 + 2 \sqrt{2}, - 4 - 2 \sqrt{2}$

Decimal Form:

$m = - 1.17157287 \dots, - 6.82842712 \dots$