y^2+3y-1.125=0

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Solution for y^2+3y-1.125=0 equation: 


Simplifying
y2 + 3y + -1.125 = 0

Reorder the terms:
-1.125 + 3y + y2 = 0

Solving
-1.125 + 3y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + 3y + 1.125 + y2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + 3y + y2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + 3y + y2 = 0 + 1.125
3y + y2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
3y + y2 = 1.125

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = 1.125 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 1.125 + 2.25

Combine like terms: 1.125 + 2.25 = 3.375
2.25 + 3y + y2 = 3.375

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 3.375

Calculate the square root of the right side: 1.837117307

Break this problem into two subproblems by setting 
(y + 1.5) equal to 1.837117307 and -1.837117307.


Subproblem 1
y + 1.5 = 1.837117307

Simplifying
y + 1.5 = 1.837117307

Reorder the terms:
1.5 + y = 1.837117307

Solving
1.5 + y = 1.837117307

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = 1.837117307 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 1.837117307 + -1.5
y = 1.837117307 + -1.5

Combine like terms: 1.837117307 + -1.5 = 0.337117307
y = 0.337117307

Simplifying
y = 0.337117307


Subproblem 2
y + 1.5 = -1.837117307

Simplifying
y + 1.5 = -1.837117307

Reorder the terms:
1.5 + y = -1.837117307

Solving
1.5 + y = -1.837117307

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = -1.837117307 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -1.837117307 + -1.5
y = -1.837117307 + -1.5

Combine like terms: -1.837117307 + -1.5 = -3.337117307
y = -3.337117307

Simplifying
y = -3.337117307


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.337117307, -3.337117307}

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