y^2+y-26=0

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


Simplifying
y2 + y + -26 = 0

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

Solving
-26 + y + 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 + y + 26 + y2 = 0 + 26

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

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

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

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
y + 0.25 + y2 = 26 + 0.25

Reorder the terms:
0.25 + y + y2 = 26 + 0.25

Combine like terms: 26 + 0.25 = 26.25
0.25 + y + y2 = 26.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(y + 0.5) equal to 5.123475383 and -5.123475383.


Subproblem 1
y + 0.5 = 5.123475383

Simplifying
y + 0.5 = 5.123475383

Reorder the terms:
0.5 + y = 5.123475383

Solving
0.5 + y = 5.123475383

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = 5.123475383 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 5.123475383 + -0.5
y = 5.123475383 + -0.5

Combine like terms: 5.123475383 + -0.5 = 4.623475383
y = 4.623475383

Simplifying
y = 4.623475383


Subproblem 2
y + 0.5 = -5.123475383

Simplifying
y + 0.5 = -5.123475383

Reorder the terms:
0.5 + y = -5.123475383

Solving
0.5 + y = -5.123475383

Solving for variable 'y'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + y = -5.123475383 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -5.123475383 + -0.5
y = -5.123475383 + -0.5

Combine like terms: -5.123475383 + -0.5 = -5.623475383
y = -5.623475383

Simplifying
y = -5.623475383


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.623475383, -5.623475383}

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