Solve for y (y+150)^2=50

${(y + 150)}^{2} = 50$

Step 1

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

$y + 150 = \pm \sqrt{50}$

Step 2

Simplify $\pm \sqrt{50}$ .

Rewrite $50$ as $5^{2} \cdot 2$ .

Factor $25$ out of $50$ .

$y + 150 = \pm \sqrt{25 (2)}$

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

$y + 150 = \pm \sqrt{5^{2} \cdot 2}$

Pull terms out from under the radical.

$y + 150 = \pm 5 \sqrt{2}$

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.

$y + 150 = 5 \sqrt{2}$

Subtract $150$ from both sides of the equation.

$y = 5 \sqrt{2} - 150$

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

$y + 150 = - 5 \sqrt{2}$

Subtract $150$ from both sides of the equation.

$y = - 5 \sqrt{2} - 150$

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

$y = 5 \sqrt{2} - 150, - 5 \sqrt{2} - 150$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = 5 \sqrt{2} - 150, - 5 \sqrt{2} - 150$

Decimal Form:

$y = - 142.92893218 \dots, - 157.07106781 \dots$