Solve Using the Square Root Property 4(x-1)^2=8

$4 {(x - 1)}^{2} = 8$

Step 1

Divide each term in $4 {(x - 1)}^{2} = 8$ by $4$ and simplify.

Divide each term in $4 {(x - 1)}^{2} = 8$ by $4$ .

$\frac{4 {(x - 1)}^{2}}{4} = \frac{8}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 {(x - 1)}^{2}}{4} = \frac{8}{4}$

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

${(x - 1)}^{2} = \frac{8}{4}$

Simplify the right side.

Divide $8$ by $4$ .

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

Step 2

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

$x - 1 = \pm \sqrt{2}$

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.

$x - 1 = \sqrt{2}$

Add $1$ to both sides of the equation.

$x = \sqrt{2} + 1$

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

$x - 1 = - \sqrt{2}$

Add $1$ to both sides of the equation.

$x = - \sqrt{2} + 1$

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

$x = \sqrt{2} + 1, - \sqrt{2} + 1$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \sqrt{2} + 1, - \sqrt{2} + 1$

Decimal Form:

$x = 2.41421356 \dots, - 0.41421356 \dots$