y^2+5y-26=0

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Solution for y^2+5y-26=0 equation: 


Simplifying
y2 + 5y + -26 = 0

Reorder the terms:
-26 + 5y + y2 = 0

Solving
-26 + 5y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + 5y + 26 + y2 = 0 + 26

Reorder the terms:
-26 + 26 + 5y + y2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + 5y + y2 = 0 + 26
5y + y2 = 0 + 26

Combine like terms: 0 + 26 = 26
5y + y2 = 26

The y term is 5y.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5y + 6.25 + y2 = 26 + 6.25

Reorder the terms:
6.25 + 5y + y2 = 26 + 6.25

Combine like terms: 26 + 6.25 = 32.25
6.25 + 5y + y2 = 32.25

Factor a perfect square on the left side:
(y + 2.5)(y + 2.5) = 32.25

Calculate the square root of the right side: 5.678908346

Break this problem into two subproblems by setting 
(y + 2.5) equal to 5.678908346 and -5.678908346.


Subproblem 1
y + 2.5 = 5.678908346

Simplifying
y + 2.5 = 5.678908346

Reorder the terms:
2.5 + y = 5.678908346

Solving
2.5 + y = 5.678908346

Solving for variable 'y'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = 5.678908346 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = 5.678908346 + -2.5
y = 5.678908346 + -2.5

Combine like terms: 5.678908346 + -2.5 = 3.178908346
y = 3.178908346

Simplifying
y = 3.178908346


Subproblem 2
y + 2.5 = -5.678908346

Simplifying
y + 2.5 = -5.678908346

Reorder the terms:
2.5 + y = -5.678908346

Solving
2.5 + y = -5.678908346

Solving for variable 'y'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + y = -5.678908346 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + y = -5.678908346 + -2.5
y = -5.678908346 + -2.5

Combine like terms: -5.678908346 + -2.5 = -8.178908346
y = -8.178908346

Simplifying
y = -8.178908346


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {3.178908346, -8.178908346}

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