Solve Using the Square Root Property (3-2x)^2=23

${(3 - 2 x)}^{2} = 23$

Step 1

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

$3 - 2 x = \pm \sqrt{23}$

Step 2

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.

$3 - 2 x = \sqrt{23}$

Subtract $3$ from both sides of the equation.

$- 2 x = \sqrt{23} - 3$

Divide each term in $- 2 x = \sqrt{23} - 3$ by $- 2$ and simplify.

Divide each term in $- 2 x = \sqrt{23} - 3$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{\sqrt{23}}{- 2} + \frac{- 3}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{\sqrt{23}}{- 2} + \frac{- 3}{- 2}$

Divide $x$ by $1$ .

$x = \frac{\sqrt{23}}{- 2} + \frac{- 3}{- 2}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$x = - \frac{\sqrt{23}}{2} + \frac{- 3}{- 2}$

Dividing two negative values results in a positive value.

$x = - \frac{\sqrt{23}}{2} + \frac{3}{2}$

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

$3 - 2 x = - \sqrt{23}$

Subtract $3$ from both sides of the equation.

$- 2 x = - \sqrt{23} - 3$

Divide each term in $- 2 x = - \sqrt{23} - 3$ by $- 2$ and simplify.

Divide each term in $- 2 x = - \sqrt{23} - 3$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- \sqrt{23}}{- 2} + \frac{- 3}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- \sqrt{23}}{- 2} + \frac{- 3}{- 2}$

Divide $x$ by $1$ .

$x = \frac{- \sqrt{23}}{- 2} + \frac{- 3}{- 2}$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$x = \frac{\sqrt{23}}{2} + \frac{- 3}{- 2}$

Dividing two negative values results in a positive value.

$x = \frac{\sqrt{23}}{2} + \frac{3}{2}$

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

$x = - \frac{\sqrt{23}}{2} + \frac{3}{2}, \frac{\sqrt{23}}{2} + \frac{3}{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{\sqrt{23}}{2} + \frac{3}{2}, \frac{\sqrt{23}}{2} + \frac{3}{2}$

Decimal Form:

$x = - 0.89791576 \dots, 3.89791576 \dots$

Solve Using the Square Root Property (3-2x)^2=23

Related Questions

Support LCMGCF.com by disabling your adblocker.