0.1x^2-x=1.1x^2+40

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Solution for 0.1x^2-x=1.1x^2+40 equation: 


Simplifying
0.1x2 + -1x = 1.1x2 + 40

Reorder the terms:
-1x + 0.1x2 = 1.1x2 + 40

Reorder the terms:
-1x + 0.1x2 = 40 + 1.1x2

Solving
-1x + 0.1x2 = 40 + 1.1x2

Solving for variable 'x'.

Reorder the terms:
-40 + -1x + 0.1x2 + -1.1x2 = 40 + 1.1x2 + -40 + -1.1x2

Combine like terms: 0.1x2 + -1.1x2 = -1x2
-40 + -1x + -1x2 = 40 + 1.1x2 + -40 + -1.1x2

Reorder the terms:
-40 + -1x + -1x2 = 40 + -40 + 1.1x2 + -1.1x2

Combine like terms: 40 + -40 = 0
-40 + -1x + -1x2 = 0 + 1.1x2 + -1.1x2
-40 + -1x + -1x2 = 1.1x2 + -1.1x2

Combine like terms: 1.1x2 + -1.1x2 = 0.0
-40 + -1x + -1x2 = 0.0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(40 + x + x2) = 0.0

Ignore the factor -1.

Subproblem 1
Set the factor '(40 + x + x2)' equal to zero and attempt to solve:

Simplifying
40 + x + x2 = 0

Solving
40 + x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-40' to each side of the equation.
40 + x + -40 + x2 = 0 + -40

Reorder the terms:
40 + -40 + x + x2 = 0 + -40

Combine like terms: 40 + -40 = 0
0 + x + x2 = 0 + -40
x + x2 = 0 + -40

Combine like terms: 0 + -40 = -40
x + x2 = -40

The x term is x.  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.
x + 0.25 + x2 = -40 + 0.25

Reorder the terms:
0.25 + x + x2 = -40 + 0.25

Combine like terms: -40 + 0.25 = -39.75
0.25 + x + x2 = -39.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -39.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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