y^2+0.7y-0.12=0

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Solution for y^2+0.7y-0.12=0 equation: 


Simplifying
y2 + 0.7y + -0.12 = 0

Reorder the terms:
-0.12 + 0.7y + y2 = 0

Solving
-0.12 + 0.7y + y2 = 0

Solving for variable 'y'.

Begin completing the square.

Move the constant term to the right:

Add '0.12' to each side of the equation.
-0.12 + 0.7y + 0.12 + y2 = 0 + 0.12

Reorder the terms:
-0.12 + 0.12 + 0.7y + y2 = 0 + 0.12

Combine like terms: -0.12 + 0.12 = 0.00
0.00 + 0.7y + y2 = 0 + 0.12
0.7y + y2 = 0 + 0.12

Combine like terms: 0 + 0.12 = 0.12
0.7y + y2 = 0.12

The y term is 0.7y.  Take half its coefficient (0.35).
Square it (0.1225) and add it to both sides.

Add '0.1225' to each side of the equation.
0.7y + 0.1225 + y2 = 0.12 + 0.1225

Reorder the terms:
0.1225 + 0.7y + y2 = 0.12 + 0.1225

Combine like terms: 0.12 + 0.1225 = 0.2425
0.1225 + 0.7y + y2 = 0.2425

Factor a perfect square on the left side:
(y + 0.35)(y + 0.35) = 0.2425

Calculate the square root of the right side: 0.49244289

Break this problem into two subproblems by setting 
(y + 0.35) equal to 0.49244289 and -0.49244289.


Subproblem 1
y + 0.35 = 0.49244289

Simplifying
y + 0.35 = 0.49244289

Reorder the terms:
0.35 + y = 0.49244289

Solving
0.35 + y = 0.49244289

Solving for variable 'y'.

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

Add '-0.35' to each side of the equation.
0.35 + -0.35 + y = 0.49244289 + -0.35

Combine like terms: 0.35 + -0.35 = 0.00
0.00 + y = 0.49244289 + -0.35
y = 0.49244289 + -0.35

Combine like terms: 0.49244289 + -0.35 = 0.14244289
y = 0.14244289

Simplifying
y = 0.14244289


Subproblem 2
y + 0.35 = -0.49244289

Simplifying
y + 0.35 = -0.49244289

Reorder the terms:
0.35 + y = -0.49244289

Solving
0.35 + y = -0.49244289

Solving for variable 'y'.

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

Add '-0.35' to each side of the equation.
0.35 + -0.35 + y = -0.49244289 + -0.35

Combine like terms: 0.35 + -0.35 = 0.00
0.00 + y = -0.49244289 + -0.35
y = -0.49244289 + -0.35

Combine like terms: -0.49244289 + -0.35 = -0.84244289
y = -0.84244289

Simplifying
y = -0.84244289


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.14244289, -0.84244289}

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