Solve Using the Square Root Property (7x-1)^2=1

${(7 x - 1)}^{2} = 1$

Step 1

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

$7 x - 1 = \pm \sqrt{1}$

Step 2

Any root of $1$ is $1$ .

$7 x - 1 = \pm 1$

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.

$7 x - 1 = 1$

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

Add $1$ to both sides of the equation.

$7 x = 1 + 1$

Add $1$ and $1$ .

$7 x = 2$

Divide each term in $7 x = 2$ by $7$ and simplify.

Divide each term in $7 x = 2$ by $7$ .

$\frac{7 x}{7} = \frac{2}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{2}{7}$

Divide $x$ by $1$ .

$x = \frac{2}{7}$

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

$7 x - 1 = - 1$

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

Add $1$ to both sides of the equation.

$7 x = - 1 + 1$

Add $- 1$ and $1$ .

$7 x = 0$

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.

$x = \frac{2}{7}, 0$

Solve Using the Square Root Property (7x-1)^2=1

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