(10y*10y)+11y-6=0

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Solution for (10y*10y)+11y-6=0 equation: 


Simplifying
(10y * 10y) + 11y + -6 = 0

Reorder the terms for easier multiplication:
(10 * 10y * y) + 11y + -6 = 0

Multiply 10 * 10
(100y * y) + 11y + -6 = 0

Multiply y * y
(100y2) + 11y + -6 = 0

Reorder the terms:
-6 + 11y + (100y2) = 0

Solving
-6 + 11y + (100y2) = 0

Solving for variable 'y'.

Begin completing the square.  Divide all terms by
100 the coefficient of the squared term: 

Divide each side by '100'.
-0.06 + 0.11y + y2 = 0.00

Move the constant term to the right:

Add '0.06' to each side of the equation.
-0.06 + 0.11y + 0.06 + y2 = 0.00 + 0.06

Reorder the terms:
-0.06 + 0.06 + 0.11y + y2 = 0.00 + 0.06

Combine like terms: -0.06 + 0.06 = 0.00
0.00 + 0.11y + y2 = 0.00 + 0.06
0.11y + y2 = 0.00 + 0.06

Combine like terms: 0.00 + 0.06 = 0.06
0.11y + y2 = 0.06

The y term is 0.11y.  Take half its coefficient (0.055).
Square it (0.003025) and add it to both sides.

Add '0.003025' to each side of the equation.
0.11y + 0.003025 + y2 = 0.06 + 0.003025

Reorder the terms:
0.003025 + 0.11y + y2 = 0.06 + 0.003025

Combine like terms: 0.06 + 0.003025 = 0.063025
0.003025 + 0.11y + y2 = 0.063025

Factor a perfect square on the left side:
((y) + 0.055)((y) + 0.055) = 0.063025

Calculate the square root of the right side: 0.251047804

Break this problem into two subproblems by setting 
((y) + 0.055) equal to 0.251047804 and -0.251047804.


Subproblem 1
(y) + 0.055 = 0.251047804

Simplifying
(y) + 0.055 = 0.251047804
y + 0.055 = 0.251047804

Reorder the terms:
0.055 + y = 0.251047804

Solving
0.055 + y = 0.251047804

Solving for variable 'y'.

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

Add '-0.055' to each side of the equation.
0.055 + -0.055 + y = 0.251047804 + -0.055

Combine like terms: 0.055 + -0.055 = 0.000
0.000 + y = 0.251047804 + -0.055
y = 0.251047804 + -0.055

Combine like terms: 0.251047804 + -0.055 = 0.196047804
y = 0.196047804

Simplifying
y = 0.196047804


Subproblem 2
(y) + 0.055 = -0.251047804

Simplifying
(y) + 0.055 = -0.251047804
y + 0.055 = -0.251047804

Reorder the terms:
0.055 + y = -0.251047804

Solving
0.055 + y = -0.251047804

Solving for variable 'y'.

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

Add '-0.055' to each side of the equation.
0.055 + -0.055 + y = -0.251047804 + -0.055

Combine like terms: 0.055 + -0.055 = 0.000
0.000 + y = -0.251047804 + -0.055
y = -0.251047804 + -0.055

Combine like terms: -0.251047804 + -0.055 = -0.306047804
y = -0.306047804

Simplifying
y = -0.306047804


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.196047804, -0.306047804}

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