Solve for y 2(y-1)^2+8=80

$2 {(y - 1)}^{2} + 8 = 80$

Step 1

Subtract $8$ from both sides of the equation.

$2 {(y - 1)}^{2} = 80 - 8$

Step 2

Subtract $8$ from $80$ .

$2 {(y - 1)}^{2} = 72$

Step 3

Divide each term in $2 {(y - 1)}^{2} = 72$ by $2$ and simplify.

Divide each term in $2 {(y - 1)}^{2} = 72$ by $2$ .

$\frac{2 {(y - 1)}^{2}}{2} = \frac{72}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 {(y - 1)}^{2}}{2} = \frac{72}{2}$

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

${(y - 1)}^{2} = \frac{72}{2}$

Simplify the right side.

Divide $72$ by $2$ .

${(y - 1)}^{2} = 36$

Step 4

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

$y - 1 = \pm \sqrt{36}$

Step 5

Simplify $\pm \sqrt{36}$ .

Rewrite $36$ as $6^{2}$ .

$y - 1 = \pm \sqrt{6^{2}}$

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

$y - 1 = \pm 6$

Step 6

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.

$y - 1 = 6$

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

Add $1$ to both sides of the equation.

$y = 6 + 1$

Add $6$ and $1$ .

$y = 7$

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

$y - 1 = - 6$

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

Add $1$ to both sides of the equation.

$y = - 6 + 1$

Add $- 6$ and $1$ .

$y = - 5$

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

$y = 7, - 5$

Solve for y 2(y-1)^2+8=80

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