y^2+y+0.7=1

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Solution for y^2+y+0.7=1 equation: 


Simplifying
y2 + y + 0.7 = 1

Reorder the terms:
0.7 + y + y2 = 1

Solving
0.7 + y + y2 = 1

Solving for variable 'y'.

Reorder the terms:
0.7 + -1 + y + y2 = 1 + -1

Combine like terms: 0.7 + -1 = -0.3
-0.3 + y + y2 = 1 + -1

Combine like terms: 1 + -1 = 0
-0.3 + y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + y + 0.3 + y2 = 0 + 0.3

Reorder the terms:
-0.3 + 0.3 + y + y2 = 0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + y + y2 = 0 + 0.3
y + y2 = 0 + 0.3

Combine like terms: 0 + 0.3 = 0.3
y + y2 = 0.3

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 = 0.3 + 0.25

Reorder the terms:
0.25 + y + y2 = 0.3 + 0.25

Combine like terms: 0.3 + 0.25 = 0.55
0.25 + y + y2 = 0.55

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = 0.55

Calculate the square root of the right side: 0.741619849

Break this problem into two subproblems by setting 
(y + 0.5) equal to 0.741619849 and -0.741619849.


Subproblem 1
y + 0.5 = 0.741619849

Simplifying
y + 0.5 = 0.741619849

Reorder the terms:
0.5 + y = 0.741619849

Solving
0.5 + y = 0.741619849

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 = 0.741619849 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = 0.741619849 + -0.5
y = 0.741619849 + -0.5

Combine like terms: 0.741619849 + -0.5 = 0.241619849
y = 0.241619849

Simplifying
y = 0.241619849


Subproblem 2
y + 0.5 = -0.741619849

Simplifying
y + 0.5 = -0.741619849

Reorder the terms:
0.5 + y = -0.741619849

Solving
0.5 + y = -0.741619849

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 = -0.741619849 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + y = -0.741619849 + -0.5
y = -0.741619849 + -0.5

Combine like terms: -0.741619849 + -0.5 = -1.241619849
y = -1.241619849

Simplifying
y = -1.241619849


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.241619849, -1.241619849}

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