0.12*x+x*x=0.9964

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Solution for 0.12*x+x*x=0.9964 equation: 


Simplifying
0.12x + x * x = 0.9964

Multiply x * x
0.12x + x2 = 0.9964

Solving
0.12x + x2 = 0.9964

Solving for variable 'x'.

Reorder the terms:
-0.9964 + 0.12x + x2 = 0.9964 + -0.9964

Combine like terms: 0.9964 + -0.9964 = 0.0000
-0.9964 + 0.12x + x2 = 0.0000

Begin completing the square.

Move the constant term to the right:

Add '0.9964' to each side of the equation.
-0.9964 + 0.12x + 0.9964 + x2 = 0.0000 + 0.9964

Reorder the terms:
-0.9964 + 0.9964 + 0.12x + x2 = 0.0000 + 0.9964

Combine like terms: -0.9964 + 0.9964 = 0.0000
0.0000 + 0.12x + x2 = 0.0000 + 0.9964
0.12x + x2 = 0.0000 + 0.9964

Combine like terms: 0.0000 + 0.9964 = 0.9964
0.12x + x2 = 0.9964

The x term is 0.12x.  Take half its coefficient (0.06).
Square it (0.0036) and add it to both sides.

Add '0.0036' to each side of the equation.
0.12x + 0.0036 + x2 = 0.9964 + 0.0036

Reorder the terms:
0.0036 + 0.12x + x2 = 0.9964 + 0.0036

Combine like terms: 0.9964 + 0.0036 = 1
0.0036 + 0.12x + x2 = 1

Factor a perfect square on the left side:
(x + 0.06)(x + 0.06) = 1

Calculate the square root of the right side: 1

Break this problem into two subproblems by setting 
(x + 0.06) equal to 1 and -1.


Subproblem 1
x + 0.06 = 1

Simplifying
x + 0.06 = 1

Reorder the terms:
0.06 + x = 1

Solving
0.06 + x = 1

Solving for variable 'x'.

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

Add '-0.06' to each side of the equation.
0.06 + -0.06 + x = 1 + -0.06

Combine like terms: 0.06 + -0.06 = 0.00
0.00 + x = 1 + -0.06
x = 1 + -0.06

Combine like terms: 1 + -0.06 = 0.94
x = 0.94

Simplifying
x = 0.94


Subproblem 2
x + 0.06 = -1

Simplifying
x + 0.06 = -1

Reorder the terms:
0.06 + x = -1

Solving
0.06 + x = -1

Solving for variable 'x'.

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

Add '-0.06' to each side of the equation.
0.06 + -0.06 + x = -1 + -0.06

Combine like terms: 0.06 + -0.06 = 0.00
0.00 + x = -1 + -0.06
x = -1 + -0.06

Combine like terms: -1 + -0.06 = -1.06
x = -1.06

Simplifying
x = -1.06


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.94, -1.06}

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