y^2+99y+620=0

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Solution for y^2+99y+620=0 equation:


Simplifying
y2 + 99y + 620 = 0

Reorder the terms:
620 + 99y + y2 = 0

Solving
620 + 99y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '-620' to each side of the equation.
620 + 99y + -620 + y2 = 0 + -620

Reorder the terms:
620 + -620 + 99y + y2 = 0 + -620

Combine like terms: 620 + -620 = 0
0 + 99y + y2 = 0 + -620
99y + y2 = 0 + -620

Combine like terms: 0 + -620 = -620
99y + y2 = -620

The y term is 99y.  Take half its coefficient (49.5).
Square it (2450.25) and add it to both sides.

Add '2450.25' to each side of the equation.
99y + 2450.25 + y2 = -620 + 2450.25

Reorder the terms:
2450.25 + 99y + y2 = -620 + 2450.25

Combine like terms: -620 + 2450.25 = 1830.25
2450.25 + 99y + y2 = 1830.25

Factor a perfect square on the left side:
(y + 49.5)(y + 49.5) = 1830.25

Calculate the square root of the right side: 42.781421201

Break this problem into two subproblems by setting 
(y + 49.5) equal to 42.781421201 and -42.781421201.

Subproblem 1

y + 49.5 = 42.781421201 Simplifying y + 49.5 = 42.781421201 Reorder the terms: 49.5 + y = 42.781421201 Solving 49.5 + y = 42.781421201 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-49.5' to each side of the equation. 49.5 + -49.5 + y = 42.781421201 + -49.5 Combine like terms: 49.5 + -49.5 = 0.0 0.0 + y = 42.781421201 + -49.5 y = 42.781421201 + -49.5 Combine like terms: 42.781421201 + -49.5 = -6.718578799 y = -6.718578799 Simplifying y = -6.718578799

Subproblem 2

y + 49.5 = -42.781421201 Simplifying y + 49.5 = -42.781421201 Reorder the terms: 49.5 + y = -42.781421201 Solving 49.5 + y = -42.781421201 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Add '-49.5' to each side of the equation. 49.5 + -49.5 + y = -42.781421201 + -49.5 Combine like terms: 49.5 + -49.5 = 0.0 0.0 + y = -42.781421201 + -49.5 y = -42.781421201 + -49.5 Combine like terms: -42.781421201 + -49.5 = -92.281421201 y = -92.281421201 Simplifying y = -92.281421201

Solution

The solution to the problem is based on the solutions from the subproblems. y = {-6.718578799, -92.281421201}

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