2x^2+1=2x+5

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


Simplifying
2x2 + 1 = 2x + 5

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

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

Solving
1 + 2x2 = 5 + 2x

Solving for variable 'x'.

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

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

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

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

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

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

Factor a trinomial.
2((-1 + -1x)(2 + -1x)) = 0

Ignore the factor 2.

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

Divide each side by '-1'.
x = -1

Simplifying
x = -1

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1, 2}

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