Solve for x 3(3x+4)^2+18=27

$3 {(3 x + 4)}^{2} + 18 = 27$

Step 1

Subtract $18$ from both sides of the equation.

$3 {(3 x + 4)}^{2} = 27 - 18$

Step 2

Subtract $18$ from $27$ .

$3 {(3 x + 4)}^{2} = 9$

Step 3

Divide each term in $3 {(3 x + 4)}^{2} = 9$ by $3$ and simplify.

Divide each term in $3 {(3 x + 4)}^{2} = 9$ by $3$ .

$\frac{3 {(3 x + 4)}^{2}}{3} = \frac{9}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 {(3 x + 4)}^{2}}{3} = \frac{9}{3}$

Divide ${(3 x + 4)}^{2}$ by $1$ .

${(3 x + 4)}^{2} = \frac{9}{3}$

Simplify the right side.

Divide $9$ by $3$ .

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

Step 4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$3 x + 4 = \pm \sqrt{3}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$3 x + 4 = \sqrt{3}$

Subtract $4$ from both sides of the equation.

$3 x = \sqrt{3} - 4$

Divide each term in $3 x = \sqrt{3} - 4$ by $3$ and simplify.

Divide each term in $3 x = \sqrt{3} - 4$ by $3$ .

$\frac{3 x}{3} = \frac{\sqrt{3}}{3} + \frac{- 4}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{\sqrt{3}}{3} + \frac{- 4}{3}$

Divide $x$ by $1$ .

$x = \frac{\sqrt{3}}{3} + \frac{- 4}{3}$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{\sqrt{3}}{3} - \frac{4}{3}$

Next, use the negative value of the $\pm$ to find the second solution.

$3 x + 4 = - \sqrt{3}$

Subtract $4$ from both sides of the equation.

$3 x = - \sqrt{3} - 4$

Divide each term in $3 x = - \sqrt{3} - 4$ by $3$ and simplify.

Divide each term in $3 x = - \sqrt{3} - 4$ by $3$ .

$\frac{3 x}{3} = \frac{- \sqrt{3}}{3} + \frac{- 4}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{- \sqrt{3}}{3} + \frac{- 4}{3}$

Divide $x$ by $1$ .

$x = \frac{- \sqrt{3}}{3} + \frac{- 4}{3}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{\sqrt{3}}{3} + \frac{- 4}{3}$

Move the negative in front of the fraction.

$x = - \frac{\sqrt{3}}{3} - \frac{4}{3}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \frac{\sqrt{3}}{3} - \frac{4}{3}, - \frac{\sqrt{3}}{3} - \frac{4}{3}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{3}}{3} - \frac{4}{3}, - \frac{\sqrt{3}}{3} - \frac{4}{3}$

Decimal Form:

$x = - 0.75598306 \dots, - 1.91068360 \dots$

Solve for x 3(3x+4)^2+18=27

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