y^2+8.5y=15

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Solution for y^2+8.5y=15 equation:


Simplifying
y2 + 8.5y = 15

Reorder the terms:
8.5y + y2 = 15

Solving
8.5y + y2 = 15

Solving for variable 'y'.

Reorder the terms:
-15 + 8.5y + y2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 8.5y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 8.5y + 15 + y2 = 0 + 15

Reorder the terms:
-15 + 15 + 8.5y + y2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 8.5y + y2 = 0 + 15
8.5y + y2 = 0 + 15

Combine like terms: 0 + 15 = 15
8.5y + y2 = 15

The y term is 8.5y.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5y + 18.0625 + y2 = 15 + 18.0625

Reorder the terms:
18.0625 + 8.5y + y2 = 15 + 18.0625

Combine like terms: 15 + 18.0625 = 33.0625
18.0625 + 8.5y + y2 = 33.0625

Factor a perfect square on the left side:
(y + 4.25)(y + 4.25) = 33.0625

Calculate the square root of the right side: 5.75

Break this problem into two subproblems by setting 
(y + 4.25) equal to 5.75 and -5.75.

Subproblem 1

y + 4.25 = 5.75 Simplifying y + 4.25 = 5.75 Reorder the terms: 4.25 + y = 5.75 Solving 4.25 + y = 5.75 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + y = 5.75 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + y = 5.75 + -4.25 y = 5.75 + -4.25 Combine like terms: 5.75 + -4.25 = 1.5 y = 1.5 Simplifying y = 1.5

Subproblem 2

y + 4.25 = -5.75 Simplifying y + 4.25 = -5.75 Reorder the terms: 4.25 + y = -5.75 Solving 4.25 + y = -5.75 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + y = -5.75 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + y = -5.75 + -4.25 y = -5.75 + -4.25 Combine like terms: -5.75 + -4.25 = -10 y = -10 Simplifying y = -10

Solution

The solution to the problem is based on the solutions from the subproblems. y = {1.5, -10}

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