Solve for x 3(4x+1)^2-37=5

$3 {(4 x + 1)}^{2} - 37 = 5$

Add $37$ to both sides of the equation.

$3 {(4 x + 1)}^{2} = 5 + 37$

Add $5$ and $37$ .

$3 {(4 x + 1)}^{2} = 42$

Divide each term in $3 {(4 x + 1)}^{2} = 42$ by $3$ and simplify.

Divide each term in $3 {(4 x + 1)}^{2} = 42$ by $3$ .

$\frac{3 {(4 x + 1)}^{2}}{3} = \frac{42}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 {(4 x + 1)}^{2}}{3} = \frac{42}{3}$

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

${(4 x + 1)}^{2} = \frac{42}{3}$

Simplify the right side.

Divide $42$ by $3$ .

${(4 x + 1)}^{2} = 14$

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

$4 x + 1 = \pm \sqrt{14}$

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.

$4 x + 1 = \sqrt{14}$

Subtract $1$ from both sides of the equation.

$4 x = \sqrt{14} - 1$

Divide each term in $4 x = \sqrt{14} - 1$ by $4$ and simplify.

Divide each term in $4 x = \sqrt{14} - 1$ by $4$ .

$\frac{4 x}{4} = \frac{\sqrt{14}}{4} + \frac{- 1}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{\sqrt{14}}{4} + \frac{- 1}{4}$

Divide $x$ by $1$ .

$x = \frac{\sqrt{14}}{4} + \frac{- 1}{4}$

Simplify the right side.

Move the negative in front of the fraction.

$x = \frac{\sqrt{14}}{4} - \frac{1}{4}$

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

$4 x + 1 = - \sqrt{14}$

Subtract $1$ from both sides of the equation.

$4 x = - \sqrt{14} - 1$

Divide each term in $4 x = - \sqrt{14} - 1$ by $4$ and simplify.

Divide each term in $4 x = - \sqrt{14} - 1$ by $4$ .

$\frac{4 x}{4} = \frac{- \sqrt{14}}{4} + \frac{- 1}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- \sqrt{14}}{4} + \frac{- 1}{4}$

Divide $x$ by $1$ .

$x = \frac{- \sqrt{14}}{4} + \frac{- 1}{4}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{\sqrt{14}}{4} + \frac{- 1}{4}$

Move the negative in front of the fraction.

$x = - \frac{\sqrt{14}}{4} - \frac{1}{4}$

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

$x = \frac{\sqrt{14}}{4} - \frac{1}{4}, - \frac{\sqrt{14}}{4} - \frac{1}{4}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{14}}{4} - \frac{1}{4}, - \frac{\sqrt{14}}{4} - \frac{1}{4}$

Decimal Form:

$x = 0.68541434 \dots, - 1.18541434 \dots$

Solve for x 3(4x+1)^2-37=5

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