Solve for x 5( square root of x-2+1)=15

$5 (\sqrt{x - 2} + 1) = 15$

Step 1

Divide each term in $5 (\sqrt{x - 2} + 1) = 15$ by $5$ and simplify.

Divide each term in $5 (\sqrt{x - 2} + 1) = 15$ by $5$ .

$\frac{5 (\sqrt{x - 2} + 1)}{5} = \frac{15}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 (\sqrt{x - 2} + 1)}{5} = \frac{15}{5}$

Divide $\sqrt{x - 2} + 1$ by $1$ .

$\sqrt{x - 2} + 1 = \frac{15}{5}$

Simplify the right side.

Divide $15$ by $5$ .

$\sqrt{x - 2} + 1 = 3$

Step 2

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

Subtract $1$ from both sides of the equation.

$\sqrt{x - 2} = 3 - 1$

Subtract $1$ from $3$ .

$\sqrt{x - 2} = 2$

Step 3

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

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

Step 4

Simplify each side of the equation.

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

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

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, ${(a^{m})}^{n} = a^{m n}$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$x - 2 = 2^{2}$

Simplify the right side.

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

$x - 2 = 4$

Step 5

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

Add $2$ to both sides of the equation.

$x = 4 + 2$

Add $4$ and $2$ .

$x = 6$

Solve for x 5( square root of x-2+1)=15

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