y^2+45.158y-188.548=0

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Solution for y^2+45.158y-188.548=0 equation: 


Simplifying
y2 + 45.158y + -188.548 = 0

Reorder the terms:
-188.548 + 45.158y + y2 = 0

Solving
-188.548 + 45.158y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '188.548' to each side of the equation.
-188.548 + 45.158y + 188.548 + y2 = 0 + 188.548

Reorder the terms:
-188.548 + 188.548 + 45.158y + y2 = 0 + 188.548

Combine like terms: -188.548 + 188.548 = 0.000
0.000 + 45.158y + y2 = 0 + 188.548
45.158y + y2 = 0 + 188.548

Combine like terms: 0 + 188.548 = 188.548
45.158y + y2 = 188.548

The y term is 45.158y.  Take half its coefficient (22.579).
Square it (509.811241) and add it to both sides.

Add '509.811241' to each side of the equation.
45.158y + 509.811241 + y2 = 188.548 + 509.811241

Reorder the terms:
509.811241 + 45.158y + y2 = 188.548 + 509.811241

Combine like terms: 188.548 + 509.811241 = 698.359241
509.811241 + 45.158y + y2 = 698.359241

Factor a perfect square on the left side:
(y + 22.579)(y + 22.579) = 698.359241

Calculate the square root of the right side: 26.426487489

Break this problem into two subproblems by setting 
(y + 22.579) equal to 26.426487489 and -26.426487489.


Subproblem 1
y + 22.579 = 26.426487489

Simplifying
y + 22.579 = 26.426487489

Reorder the terms:
22.579 + y = 26.426487489

Solving
22.579 + y = 26.426487489

Solving for variable 'y'.

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

Add '-22.579' to each side of the equation.
22.579 + -22.579 + y = 26.426487489 + -22.579

Combine like terms: 22.579 + -22.579 = 0.000
0.000 + y = 26.426487489 + -22.579
y = 26.426487489 + -22.579

Combine like terms: 26.426487489 + -22.579 = 3.847487489
y = 3.847487489

Simplifying
y = 3.847487489


Subproblem 2
y + 22.579 = -26.426487489

Simplifying
y + 22.579 = -26.426487489

Reorder the terms:
22.579 + y = -26.426487489

Solving
22.579 + y = -26.426487489

Solving for variable 'y'.

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

Add '-22.579' to each side of the equation.
22.579 + -22.579 + y = -26.426487489 + -22.579

Combine like terms: 22.579 + -22.579 = 0.000
0.000 + y = -26.426487489 + -22.579
y = -26.426487489 + -22.579

Combine like terms: -26.426487489 + -22.579 = -49.005487489
y = -49.005487489

Simplifying
y = -49.005487489


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.847487489, -49.005487489}

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