-1=2x^2-4x+5

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Solution for -1=2x^2-4x+5 equation: 


Simplifying
-1 = 2x2 + -4x + 5

Reorder the terms:
-1 = 5 + -4x + 2x2

Solving
-1 = 5 + -4x + 2x2

Solving for variable 'x'.

Combine like terms: -1 + -5 = -6
-6 + 4x + -2x2 = 5 + -4x + 2x2 + -5 + 4x + -2x2

Reorder the terms:
-6 + 4x + -2x2 = 5 + -5 + -4x + 4x + 2x2 + -2x2

Combine like terms: 5 + -5 = 0
-6 + 4x + -2x2 = 0 + -4x + 4x + 2x2 + -2x2
-6 + 4x + -2x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
-6 + 4x + -2x2 = 0 + 2x2 + -2x2
-6 + 4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-6 + 4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 2x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-3 + 2x + -1x2)' equal to zero and attempt to solve:

Simplifying
-3 + 2x + -1x2 = 0

Solving
-3 + 2x + -1x2 = 0

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

Divide each side by '-1'.
3 + -2x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -2x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -2x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x + x2 = 0 + -3
-2x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2x + x2 = -3

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -3 + 1

Reorder the terms:
1 + -2x + x2 = -3 + 1

Combine like terms: -3 + 1 = -2
1 + -2x + x2 = -2

Factor a perfect square on the left side:
(x + -1)(x + -1) = -2

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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