2x^2+1=2x+12

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Solution for 2x^2+1=2x+12 equation:


Simplifying
2x2 + 1 = 2x + 12

Reorder the terms:
1 + 2x2 = 2x + 12

Reorder the terms:
1 + 2x2 = 12 + 2x

Solving
1 + 2x2 = 12 + 2x

Solving for variable 'x'.

Reorder the terms:
1 + -12 + -2x + 2x2 = 12 + 2x + -12 + -2x

Combine like terms: 1 + -12 = -11
-11 + -2x + 2x2 = 12 + 2x + -12 + -2x

Reorder the terms:
-11 + -2x + 2x2 = 12 + -12 + 2x + -2x

Combine like terms: 12 + -12 = 0
-11 + -2x + 2x2 = 0 + 2x + -2x
-11 + -2x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-11 + -2x + 2x2 = 0

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

Divide each side by '2'.
-5.5 + -1x + x2 = 0

Move the constant term to the right:

Add '5.5' to each side of the equation.
-5.5 + -1x + 5.5 + x2 = 0 + 5.5

Reorder the terms:
-5.5 + 5.5 + -1x + x2 = 0 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + -1x + x2 = 0 + 5.5
-1x + x2 = 0 + 5.5

Combine like terms: 0 + 5.5 = 5.5
-1x + x2 = 5.5

The x term is -1x.  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 = 5.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 5.5 + 0.25

Combine like terms: 5.5 + 0.25 = 5.75
0.25 + -1x + x2 = 5.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 5.75

Calculate the square root of the right side: 2.397915762

Break this problem into two subproblems by setting 
(x + -0.5) equal to 2.397915762 and -2.397915762.

Subproblem 1

x + -0.5 = 2.397915762 Simplifying x + -0.5 = 2.397915762 Reorder the terms: -0.5 + x = 2.397915762 Solving -0.5 + x = 2.397915762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 2.397915762 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.397915762 + 0.5 x = 2.397915762 + 0.5 Combine like terms: 2.397915762 + 0.5 = 2.897915762 x = 2.897915762 Simplifying x = 2.897915762

Subproblem 2

x + -0.5 = -2.397915762 Simplifying x + -0.5 = -2.397915762 Reorder the terms: -0.5 + x = -2.397915762 Solving -0.5 + x = -2.397915762 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -2.397915762 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.397915762 + 0.5 x = -2.397915762 + 0.5 Combine like terms: -2.397915762 + 0.5 = -1.897915762 x = -1.897915762 Simplifying x = -1.897915762

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.897915762, -1.897915762}

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