Solve for x 9(5x+2)^2-42=7

$9 {(5 x + 2)}^{2} - 42 = 7$

Add $42$ to both sides of the equation.

$9 {(5 x + 2)}^{2} = 7 + 42$

Add $7$ and $42$ .

$9 {(5 x + 2)}^{2} = 49$

Divide each term in $9 {(5 x + 2)}^{2} = 49$ by $9$ and simplify.

Divide each term in $9 {(5 x + 2)}^{2} = 49$ by $9$ .

$\frac{9 {(5 x + 2)}^{2}}{9} = \frac{49}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 {(5 x + 2)}^{2}}{9} = \frac{49}{9}$

Divide ${(5 x + 2)}^{2}$ by $1$ .

${(5 x + 2)}^{2} = \frac{49}{9}$

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

$5 x + 2 = \pm \sqrt{\frac{49}{9}}$

Simplify $\pm \sqrt{\frac{49}{9}}$ .

Rewrite $\sqrt{\frac{49}{9}}$ as $\frac{\sqrt{49}}{\sqrt{9}}$ .

$5 x + 2 = \pm \frac{\sqrt{49}}{\sqrt{9}}$

Simplify the numerator.

Rewrite $49$ as $7^{2}$ .

$5 x + 2 = \pm \frac{\sqrt{7^{2}}}{\sqrt{9}}$

Pull terms out from under the radical, assuming positive real numbers.

$5 x + 2 = \pm \frac{7}{\sqrt{9}}$

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

$5 x + 2 = \pm \frac{7}{\sqrt{3^{2}}}$

Pull terms out from under the radical, assuming positive real numbers.

$5 x + 2 = \pm \frac{7}{3}$

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.

$5 x + 2 = \frac{7}{3}$

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

Subtract $2$ from both sides of the equation.

$5 x = \frac{7}{3} - 2$

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$5 x = \frac{7}{3} - 2 \cdot \frac{3}{3}$

Combine $- 2$ and $\frac{3}{3}$ .

$5 x = \frac{7}{3} + \frac{- 2 \cdot 3}{3}$

Combine the numerators over the common denominator.

$5 x = \frac{7 - 2 \cdot 3}{3}$

Simplify the numerator.

Multiply $- 2$ by $3$ .

$5 x = \frac{7 - 6}{3}$

Subtract $6$ from $7$ .

$5 x = \frac{1}{3}$

Divide each term in $5 x = \frac{1}{3}$ by $5$ and simplify.

Divide each term in $5 x = \frac{1}{3}$ by $5$ .

$\frac{5 x}{5} = \frac{\frac{1}{3}}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{\frac{1}{3}}{5}$

Divide $x$ by $1$ .

$x = \frac{\frac{1}{3}}{5}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{1}{3} \cdot \frac{1}{5}$

Multiply $\frac{1}{3} \cdot \frac{1}{5}$ .

Multiply $\frac{1}{3}$ by $\frac{1}{5}$ .

$x = \frac{1}{3 \cdot 5}$

Multiply $3$ by $5$ .

$x = \frac{1}{15}$

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

$5 x + 2 = - \frac{7}{3}$

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

Subtract $2$ from both sides of the equation.

$5 x = - \frac{7}{3} - 2$

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$5 x = - \frac{7}{3} - 2 \cdot \frac{3}{3}$

Combine $- 2$ and $\frac{3}{3}$ .

$5 x = - \frac{7}{3} + \frac{- 2 \cdot 3}{3}$

Combine the numerators over the common denominator.

$5 x = \frac{- 7 - 2 \cdot 3}{3}$

Simplify the numerator.

Multiply $- 2$ by $3$ .

$5 x = \frac{- 7 - 6}{3}$

Subtract $6$ from $- 7$ .

$5 x = \frac{- 13}{3}$

Move the negative in front of the fraction.

$5 x = - \frac{13}{3}$

Divide each term in $5 x = - \frac{13}{3}$ by $5$ and simplify.

Divide each term in $5 x = - \frac{13}{3}$ by $5$ .

$\frac{5 x}{5} = \frac{- \frac{13}{3}}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- \frac{13}{3}}{5}$

Divide $x$ by $1$ .

$x = \frac{- \frac{13}{3}}{5}$

Simplify the right side.

Multiply the numerator by the reciprocal of the denominator.

$x = - \frac{13}{3} \cdot \frac{1}{5}$

Multiply $- \frac{13}{3} \cdot \frac{1}{5}$ .

Multiply $\frac{1}{5}$ by $\frac{13}{3}$ .

$x = - \frac{13}{5 \cdot 3}$

Multiply $5$ by $3$ .

$x = - \frac{13}{15}$

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

$x = \frac{1}{15}, - \frac{13}{15}$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{15}, - \frac{13}{15}$

Decimal Form:

$x = 0.0\overline{6}, - 0.8\overline{6}$

Solve for x 9(5x+2)^2-42=7

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