Solve for x 3(x+5)^(1/2)-6=0

$3 {(x + 5)}^{\frac{1}{2}} - 6 = 0$

Step 1

Add $6$ to both sides of the equation.

$3 {(x + 5)}^{\frac{1}{2}} = 6$

Step 2

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

${(3 {(x + 5)}^{\frac{1}{2}})}^{2} = 6^{2}$

Step 3

Simplify the exponent.

Simplify the left side.

Simplify ${(3 {(x + 5)}^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $3 {(x + 5)}^{\frac{1}{2}}$ .

$3^{2} {({(x + 5)}^{\frac{1}{2}})}^{2} = 6^{2}$

Raise $3$ to the power of $2$ .

$9 {({(x + 5)}^{\frac{1}{2}})}^{2} = 6^{2}$

Multiply the exponents in ${({(x + 5)}^{\frac{1}{2}})}^{2}$ .

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

$9 {(x + 5)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$9 {(x + 5)}^{\frac{1}{2} \cdot 2} = 6^{2}$

Rewrite the expression.

$9 {(x + 5)}^{1} = 6^{2}$

Simplify.

$9 (x + 5) = 6^{2}$

Apply the distributive property.

$9 x + 9 \cdot 5 = 6^{2}$

Multiply $9$ by $5$ .

$9 x + 45 = 6^{2}$

Simplify the right side.

Raise $6$ to the power of $2$ .

$9 x + 45 = 36$

Step 4

Solve for $x$ .

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

Subtract $45$ from both sides of the equation.

$9 x = 36 - 45$

Subtract $45$ from $36$ .

$9 x = - 9$

Divide each term in $9 x = - 9$ by $9$ and simplify.

Divide each term in $9 x = - 9$ by $9$ .

$\frac{9 x}{9} = \frac{- 9}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{- 9}{9}$

Divide $x$ by $1$ .

$x = \frac{- 9}{9}$

Simplify the right side.

Divide $- 9$ by $9$ .

$x = - 1$

Solve for x 3(x+5)^(1/2)-6=0

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