1(y^2+13y-90)=3

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Solution for 1(y^2+13y-90)=3 equation: 


Simplifying
1(y2 + 13y + -90) = 3

Reorder the terms:
1(-90 + 13y + y2) = 3
(-90 * 1 + 13y * 1 + y2 * 1) = 3
(-90 + 13y + 1y2) = 3

Solving
-90 + 13y + 1y2 = 3

Solving for variable 'y'.

Reorder the terms:
-90 + -3 + 13y + 1y2 = 3 + -3

Combine like terms: -90 + -3 = -93
-93 + 13y + 1y2 = 3 + -3

Combine like terms: 3 + -3 = 0
-93 + 13y + 1y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '93' to each side of the equation.
-93 + 13y + 93 + y2 = 0 + 93

Reorder the terms:
-93 + 93 + 13y + y2 = 0 + 93

Combine like terms: -93 + 93 = 0
0 + 13y + y2 = 0 + 93
13y + y2 = 0 + 93

Combine like terms: 0 + 93 = 93
13y + y2 = 93

The y term is 13y.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13y + 42.25 + y2 = 93 + 42.25

Reorder the terms:
42.25 + 13y + y2 = 93 + 42.25

Combine like terms: 93 + 42.25 = 135.25
42.25 + 13y + y2 = 135.25

Factor a perfect square on the left side:
(y + 6.5)(y + 6.5) = 135.25

Calculate the square root of the right side: 11.62970335

Break this problem into two subproblems by setting 
(y + 6.5) equal to 11.62970335 and -11.62970335.


Subproblem 1
y + 6.5 = 11.62970335

Simplifying
y + 6.5 = 11.62970335

Reorder the terms:
6.5 + y = 11.62970335

Solving
6.5 + y = 11.62970335

Solving for variable 'y'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + y = 11.62970335 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + y = 11.62970335 + -6.5
y = 11.62970335 + -6.5

Combine like terms: 11.62970335 + -6.5 = 5.12970335
y = 5.12970335

Simplifying
y = 5.12970335


Subproblem 2
y + 6.5 = -11.62970335

Simplifying
y + 6.5 = -11.62970335

Reorder the terms:
6.5 + y = -11.62970335

Solving
6.5 + y = -11.62970335

Solving for variable 'y'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + y = -11.62970335 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + y = -11.62970335 + -6.5
y = -11.62970335 + -6.5

Combine like terms: -11.62970335 + -6.5 = -18.12970335
y = -18.12970335

Simplifying
y = -18.12970335


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {5.12970335, -18.12970335}

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