Solve by Factoring square root of x-2+1=5

$\sqrt{x - 2} + 1 = 5$

Step 1

Subtract $5$ from both sides of the equation.

$\sqrt{x - 2} + 1 - 5 = 0$

Step 2

Subtract $5$ from $1$ .

$\sqrt{x - 2} - 4 = 0$

Step 3

Add $4$ to both sides of the equation.

$\sqrt{x - 2} = 4$

Step 4

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

${\sqrt{x - 2}}^{2} = 4^{2}$

Step 5

Simplify each side of the equation.

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

${({(x - 2)}^{\frac{1}{2}})}^{2} = 4^{2}$

Simplify the left side.

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

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

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

${(x - 2)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(x - 2)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Rewrite the expression.

${(x - 2)}^{1} = 4^{2}$

Simplify.

$x - 2 = 4^{2}$

Simplify the right side.

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

$x - 2 = 16$

Step 6

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

Add $2$ to both sides of the equation.

$x = 16 + 2$

Add $16$ and $2$ .

$x = 18$