Solve for m square root of m-7=n+3

$\sqrt{m - 7} = n + 3$

Step 1

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

${\sqrt{m - 7}}^{2} = {(n + 3)}^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{m - 7}$ as ${(m - 7)}^{\frac{1}{2}}$ .

${({(m - 7)}^{\frac{1}{2}})}^{2} = {(n + 3)}^{2}$

Simplify the left side.

Simplify ${({(m - 7)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(m - 7)}^{\frac{1}{2}})}^{2}$ .

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

${(m - 7)}^{\frac{1}{2} \cdot 2} = {(n + 3)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(m - 7)}^{\frac{1}{2} \cdot 2} = {(n + 3)}^{2}$

Rewrite the expression.

${(m - 7)}^{1} = {(n + 3)}^{2}$

Simplify.

$m - 7 = {(n + 3)}^{2}$

Simplify the right side.

Simplify ${(n + 3)}^{2}$ .

Rewrite ${(n + 3)}^{2}$ as $(n + 3) (n + 3)$ .

$m - 7 = (n + 3) (n + 3)$

Expand $(n + 3) (n + 3)$ using the FOIL Method.

Apply the distributive property.

$m - 7 = n (n + 3) + 3 (n + 3)$

Apply the distributive property.

$m - 7 = n \cdot n + n \cdot 3 + 3 (n + 3)$

Apply the distributive property.

$m - 7 = n \cdot n + n \cdot 3 + 3 n + 3 \cdot 3$

Simplify and combine like terms.

Simplify each term.

Multiply $n$ by $n$ .

$m - 7 = n^{2} + n \cdot 3 + 3 n + 3 \cdot 3$

Move $3$ to the left of $n$ .

$m - 7 = n^{2} + 3 \cdot n + 3 n + 3 \cdot 3$

Multiply $3$ by $3$ .

$m - 7 = n^{2} + 3 n + 3 n + 9$

Add $3 n$ and $3 n$ .

$m - 7 = n^{2} + 6 n + 9$

Step 3

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

Add $7$ to both sides of the equation.

$m = n^{2} + 6 n + 9 + 7$

Add $9$ and $7$ .

$m = n^{2} + 6 n + 16$

Solve for m square root of m-7=n+3

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