Solve by Factoring square root of 3x+54+6=2

$\sqrt{3 x + 54} + 6 = 2$

Step 1

Subtract $2$ from both sides of the equation.

$\sqrt{3 x + 54} + 6 - 2 = 0$

Step 2

Simplify $\sqrt{3 x + 54} + 6 - 2$ .

Factor $3$ out of $3 x + 54$ .

Factor $3$ out of $3 x$ .

$\sqrt{3 (x) + 54} + 6 - 2 = 0$

Factor $3$ out of $54$ .

$\sqrt{3 x + 3 \cdot 18} + 6 - 2 = 0$

Factor $3$ out of $3 x + 3 \cdot 18$ .

$\sqrt{3 (x + 18)} + 6 - 2 = 0$

Subtract $2$ from $6$ .

$\sqrt{3 (x + 18)} + 4 = 0$

Step 3

Subtract $4$ from both sides of the equation.

$\sqrt{3 (x + 18)} = - 4$

Step 4

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

${\sqrt{3 (x + 18)}}^{2} = {(- 4)}^{2}$

Step 5

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 (x + 18)}$ as ${(3 (x + 18))}^{\frac{1}{2}}$ .

${({(3 (x + 18))}^{\frac{1}{2}})}^{2} = {(- 4)}^{2}$

Simplify the left side.

Simplify ${({(3 (x + 18))}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 (x + 18))}^{\frac{1}{2}})}^{2}$ .

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

${(3 (x + 18))}^{\frac{1}{2} \cdot 2} = {(- 4)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 (x + 18))}^{\frac{1}{2} \cdot 2} = {(- 4)}^{2}$

Rewrite the expression.

${(3 (x + 18))}^{1} = {(- 4)}^{2}$

Apply the distributive property.

${(3 x + 3 \cdot 18)}^{1} = {(- 4)}^{2}$

Multiply.

Multiply $3$ by $18$ .

${(3 x + 54)}^{1} = {(- 4)}^{2}$

Simplify.

$3 x + 54 = {(- 4)}^{2}$

Simplify the right side.

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

$3 x + 54 = 16$

Step 6

Solve for $x$ .

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

Subtract $54$ from both sides of the equation.

$3 x = 16 - 54$

Subtract $54$ from $16$ .

$3 x = - 38$

Divide each term in $3 x = - 38$ by $3$ and simplify.

Divide each term in $3 x = - 38$ by $3$ .

$\frac{3 x}{3} = \frac{- 38}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 38}{3}$

Divide $x$ by $1$ .

$x = \frac{- 38}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{38}{3}$

Step 7

Exclude the solutions that do not make $\sqrt{3 (x + 18)} + 4 = 0$ true.

$No solution$

Solve by Factoring square root of 3x+54+6=2

Related Questions

Support LCMGCF.com by disabling your adblocker.