y^2+9y-62=0

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Solution for y^2+9y-62=0 equation: 


Simplifying
y2 + 9y + -62 = 0

Reorder the terms:
-62 + 9y + y2 = 0

Solving
-62 + 9y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '62' to each side of the equation.
-62 + 9y + 62 + y2 = 0 + 62

Reorder the terms:
-62 + 62 + 9y + y2 = 0 + 62

Combine like terms: -62 + 62 = 0
0 + 9y + y2 = 0 + 62
9y + y2 = 0 + 62

Combine like terms: 0 + 62 = 62
9y + y2 = 62

The y term is 9y.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9y + 20.25 + y2 = 62 + 20.25

Reorder the terms:
20.25 + 9y + y2 = 62 + 20.25

Combine like terms: 62 + 20.25 = 82.25
20.25 + 9y + y2 = 82.25

Factor a perfect square on the left side:
(y + 4.5)(y + 4.5) = 82.25

Calculate the square root of the right side: 9.069178574

Break this problem into two subproblems by setting 
(y + 4.5) equal to 9.069178574 and -9.069178574.


Subproblem 1
y + 4.5 = 9.069178574

Simplifying
y + 4.5 = 9.069178574

Reorder the terms:
4.5 + y = 9.069178574

Solving
4.5 + y = 9.069178574

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-4.5' to each side of the equation.
4.5 + -4.5 + y = 9.069178574 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + y = 9.069178574 + -4.5
y = 9.069178574 + -4.5

Combine like terms: 9.069178574 + -4.5 = 4.569178574
y = 4.569178574

Simplifying
y = 4.569178574


Subproblem 2
y + 4.5 = -9.069178574

Simplifying
y + 4.5 = -9.069178574

Reorder the terms:
4.5 + y = -9.069178574

Solving
4.5 + y = -9.069178574

Solving for variable 'y'.

Move all terms containing y to the left, all other terms to the right.

Add '-4.5' to each side of the equation.
4.5 + -4.5 + y = -9.069178574 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + y = -9.069178574 + -4.5
y = -9.069178574 + -4.5

Combine like terms: -9.069178574 + -4.5 = -13.569178574
y = -13.569178574

Simplifying
y = -13.569178574


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.569178574, -13.569178574}

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