Solve Using the Square Root Property (7x-3)^2=9

${(7 x - 3)}^{2} = 9$

Step 1

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

$7 x - 3 = \pm \sqrt{9}$

Step 2

Simplify $\pm \sqrt{9}$ .

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

$7 x - 3 = \pm \sqrt{3^{2}}$

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

$7 x - 3 = \pm 3$

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.

$7 x - 3 = 3$

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

Add $3$ to both sides of the equation.

$7 x = 3 + 3$

Add $3$ and $3$ .

$7 x = 6$

Divide each term in $7 x = 6$ by $7$ and simplify.

Divide each term in $7 x = 6$ by $7$ .

$\frac{7 x}{7} = \frac{6}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{6}{7}$

Divide $x$ by $1$ .

$x = \frac{6}{7}$

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

$7 x - 3 = - 3$

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

Add $3$ to both sides of the equation.

$7 x = - 3 + 3$

Add $- 3$ and $3$ .

$7 x = 0$

Divide each term in $7 x = 0$ by $7$ and simplify.

Divide each term in $7 x = 0$ by $7$ .

$\frac{7 x}{7} = \frac{0}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{0}{7}$

Divide $x$ by $1$ .

$x = \frac{0}{7}$

Simplify the right side.

Divide $0$ by $7$ .

$x = 0$

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

$x = \frac{6}{7}, 0$

Solve Using the Square Root Property (7x-3)^2=9

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