Solve for y (3-2y)^2=3

${(3 - 2 y)}^{2} = 3$

Step 1

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

$3 - 2 y = \pm \sqrt{3}$

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.

$3 - 2 y = \sqrt{3}$

Subtract $3$ from both sides of the equation.

$- 2 y = \sqrt{3} - 3$

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

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

$\frac{- 2 y}{- 2} = \frac{\sqrt{3}}{- 2} + \frac{- 3}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{\sqrt{3}}{- 2} + \frac{- 3}{- 2}$

Divide $y$ by $1$ .

$y = \frac{\sqrt{3}}{- 2} + \frac{- 3}{- 2}$

Simplify the right side.

Simplify each term.

Move the negative in front of the fraction.

$y = - \frac{\sqrt{3}}{2} + \frac{- 3}{- 2}$

Dividing two negative values results in a positive value.

$y = - \frac{\sqrt{3}}{2} + \frac{3}{2}$

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

$3 - 2 y = - \sqrt{3}$

Subtract $3$ from both sides of the equation.

$- 2 y = - \sqrt{3} - 3$

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

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

$\frac{- 2 y}{- 2} = \frac{- \sqrt{3}}{- 2} + \frac{- 3}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- \sqrt{3}}{- 2} + \frac{- 3}{- 2}$

Divide $y$ by $1$ .

$y = \frac{- \sqrt{3}}{- 2} + \frac{- 3}{- 2}$

Simplify the right side.

Simplify each term.

Dividing two negative values results in a positive value.

$y = \frac{\sqrt{3}}{2} + \frac{- 3}{- 2}$

Dividing two negative values results in a positive value.

$y = \frac{\sqrt{3}}{2} + \frac{3}{2}$

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

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = 0.63397459 \dots, 2.36602540 \dots$

Solve for y (3-2y)^2=3

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