2x+6=2x^2+100

Solution for 2x+6=2x^2+100 equation:

Simplifying
2x + 6 = 2x2 + 100

Reorder the terms:
6 + 2x = 2x2 + 100

Reorder the terms:
6 + 2x = 100 + 2x2

Solving
6 + 2x = 100 + 2x2

Solving for variable 'x'.

Reorder the terms:
6 + -100 + 2x + -2x2 = 100 + 2x2 + -100 + -2x2

Combine like terms: 6 + -100 = -94
-94 + 2x + -2x2 = 100 + 2x2 + -100 + -2x2

Reorder the terms:
-94 + 2x + -2x2 = 100 + -100 + 2x2 + -2x2

Combine like terms: 100 + -100 = 0
-94 + 2x + -2x2 = 0 + 2x2 + -2x2
-94 + 2x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-94 + 2x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-47 + x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-47 + x + -1x2)' equal to zero and attempt to solve:

Simplifying
-47 + x + -1x2 = 0

Solving
-47 + x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
47 + -1x + x2 = 0

Move the constant term to the right:

Add '-47' to each side of the equation.
47 + -1x + -47 + x2 = 0 + -47

Reorder the terms:
47 + -47 + -1x + x2 = 0 + -47

Combine like terms: 47 + -47 = 0
0 + -1x + x2 = 0 + -47
-1x + x2 = 0 + -47

Combine like terms: 0 + -47 = -47
-1x + x2 = -47

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.
-1x + 0.25 + x2 = -47 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -47 + 0.25

Combine like terms: -47 + 0.25 = -46.75
0.25 + -1x + x2 = -46.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -46.75

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.