Solve for m 1-2 square root of m+12=5

$1 - 2 \sqrt{m + 12} = 5$

Step 1

Move all terms not containing $- 2 \sqrt{m + 12}$ to the right side of the equation.

Subtract $1$ from both sides of the equation.

$- 2 \sqrt{m + 12} = 5 - 1$

Subtract $1$ from $5$ .

$- 2 \sqrt{m + 12} = 4$

Step 2

To remove the radical on the left side of the equation, square both sides of the equation.

${(- 2 \sqrt{m + 12})}^{2} = 4^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{m + 12}$ as ${(m + 12)}^{\frac{1}{2}}$ .

${(- 2 {(m + 12)}^{\frac{1}{2}})}^{2} = 4^{2}$

Simplify the left side.

Simplify ${(- 2 {(m + 12)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $- 2 {(m + 12)}^{\frac{1}{2}}$ .

${(- 2)}^{2} {({(m + 12)}^{\frac{1}{2}})}^{2} = 4^{2}$

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

$4 {({(m + 12)}^{\frac{1}{2}})}^{2} = 4^{2}$

Multiply the exponents in ${({(m + 12)}^{\frac{1}{2}})}^{2}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$4 {(m + 12)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$4 {(m + 12)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Rewrite the expression.

$4 {(m + 12)}^{1} = 4^{2}$

Simplify.

$4 (m + 12) = 4^{2}$

Apply the distributive property.

$4 m + 4 \cdot 12 = 4^{2}$

Multiply $4$ by $12$ .

$4 m + 48 = 4^{2}$

Simplify the right side.

Raise $4$ to the power of $2$ .

$4 m + 48 = 16$

Step 4

Solve for $m$ .

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

Subtract $48$ from both sides of the equation.

$4 m = 16 - 48$

Subtract $48$ from $16$ .

$4 m = - 32$

Divide each term in $4 m = - 32$ by $4$ and simplify.

Divide each term in $4 m = - 32$ by $4$ .

$\frac{4 m}{4} = \frac{- 32}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 m}{4} = \frac{- 32}{4}$

Divide $m$ by $1$ .

$m = \frac{- 32}{4}$

Simplify the right side.

Divide $- 32$ by $4$ .

$m = - 8$

Step 5

Exclude the solutions that do not make $1 - 2 \sqrt{m + 12} = 5$ true.

$No solution$

Solve for m 1-2 square root of m+12=5

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