Solve for y (4y-5)^2=25

${(4 y - 5)}^{2} = 25$

Step 1

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

$4 y - 5 = \pm \sqrt{25}$

Step 2

Simplify $\pm \sqrt{25}$ .

Rewrite $25$ as $5^{2}$ .

$4 y - 5 = \pm \sqrt{5^{2}}$

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

$4 y - 5 = \pm 5$

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.

$4 y - 5 = 5$

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

Add $5$ to both sides of the equation.

$4 y = 5 + 5$

Add $5$ and $5$ .

$4 y = 10$

Divide each term in $4 y = 10$ by $4$ and simplify.

Divide each term in $4 y = 10$ by $4$ .

$\frac{4 y}{4} = \frac{10}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{10}{4}$

Divide $y$ by $1$ .

$y = \frac{10}{4}$

Simplify the right side.

Cancel the common factor of $10$ and $4$ .

Factor $2$ out of $10$ .

$y = \frac{2 (5)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$y = \frac{2 \cdot 5}{2 \cdot 2}$

Cancel the common factor.

$y = \frac{2 \cdot 5}{2 \cdot 2}$

Rewrite the expression.

$y = \frac{5}{2}$

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

$4 y - 5 = - 5$

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

Add $5$ to both sides of the equation.

$4 y = - 5 + 5$

Add $- 5$ and $5$ .

$4 y = 0$

Divide each term in $4 y = 0$ by $4$ and simplify.

Divide each term in $4 y = 0$ by $4$ .

$\frac{4 y}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{0}{4}$

Divide $y$ by $1$ .

$y = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$y = 0$

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

$y = \frac{5}{2}, 0$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{5}{2}, 0$

Decimal Form:

$y = 2.5, 0$

Mixed Number Form:

$y = 2 \frac{1}{2}, 0$

Solve for y (4y-5)^2=25

Related Questions