Solve Using the Square Root Property (9x-2)^2=4

${(9 x - 2)}^{2} = 4$

Step 1

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

$9 x - 2 = \pm \sqrt{4}$

Step 2

Simplify $\pm \sqrt{4}$ .

Rewrite $4$ as $2^{2}$ .

$9 x - 2 = \pm \sqrt{2^{2}}$

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

$9 x - 2 = \pm 2$

Step 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.

$9 x - 2 = 2$

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

Add $2$ to both sides of the equation.

$9 x = 2 + 2$

Add $2$ and $2$ .

$9 x = 4$

Divide each term in $9 x = 4$ by $9$ and simplify.

Divide each term in $9 x = 4$ by $9$ .

$\frac{9 x}{9} = \frac{4}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{4}{9}$

Divide $x$ by $1$ .

$x = \frac{4}{9}$

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

$9 x - 2 = - 2$

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

Add $2$ to both sides of the equation.

$9 x = - 2 + 2$

Add $- 2$ and $2$ .

$9 x = 0$

Divide each term in $9 x = 0$ by $9$ and simplify.

Divide each term in $9 x = 0$ by $9$ .

$\frac{9 x}{9} = \frac{0}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 x}{9} = \frac{0}{9}$

Divide $x$ by $1$ .

$x = \frac{0}{9}$

Simplify the right side.

Divide $0$ by $9$ .

$x = 0$

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

$x = \frac{4}{9}, 0$

Solve Using the Square Root Property (9x-2)^2=4

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