Solve for a 10+ square root of a+7=11

$10 + \sqrt{a + 7} = 11$

Step 1

Move all terms not containing $\sqrt{a + 7}$ to the right side of the equation.

Subtract $10$ from both sides of the equation.

$\sqrt{a + 7} = 11 - 10$

Subtract $10$ from $11$ .

$\sqrt{a + 7} = 1$

Step 2

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

${\sqrt{a + 7}}^{2} = 1^{2}$

Step 3

Simplify each side of the equation.

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

${({(a + 7)}^{\frac{1}{2}})}^{2} = 1^{2}$

Simplify the left side.

Simplify ${({(a + 7)}^{\frac{1}{2}})}^{2}$ .

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

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

${(a + 7)}^{\frac{1}{2} \cdot 2} = 1^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(a + 7)}^{\frac{1}{2} \cdot 2} = 1^{2}$

Rewrite the expression.

${(a + 7)}^{1} = 1^{2}$

Simplify.

$a + 7 = 1^{2}$

Simplify the right side.

One to any power is one.

$a + 7 = 1$

Step 4

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

Subtract $7$ from both sides of the equation.

$a = 1 - 7$

Subtract $7$ from $1$ .

$a = - 6$