2=x^2+0.5x

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Solution for 2=x^2+0.5x equation:


Simplifying
2 = x2 + 0.5x

Reorder the terms:
2 = 0.5x + x2

Solving
2 = 0.5x + x2

Solving for variable 'x'.

Reorder the terms:
2 + -0.5x + -1x2 = 0.5x + -0.5x + x2 + -1x2

Combine like terms: 0.5x + -0.5x = 0.0
2 + -0.5x + -1x2 = 0.0 + x2 + -1x2
2 + -0.5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + -0.5x + -1x2 = 0

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

Divide each side by '-1'.
-2 + 0.5x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 0.5x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 0.5x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 0.5x + x2 = 0 + 2
0.5x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
0.5x + x2 = 2

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 2 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 2 + 0.0625

Combine like terms: 2 + 0.0625 = 2.0625
0.0625 + 0.5x + x2 = 2.0625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.436140662 and -1.436140662.

Subproblem 1

x + 0.25 = 1.436140662 Simplifying x + 0.25 = 1.436140662 Reorder the terms: 0.25 + x = 1.436140662 Solving 0.25 + x = 1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 1.436140662 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 1.436140662 + -0.25 x = 1.436140662 + -0.25 Combine like terms: 1.436140662 + -0.25 = 1.186140662 x = 1.186140662 Simplifying x = 1.186140662

Subproblem 2

x + 0.25 = -1.436140662 Simplifying x + 0.25 = -1.436140662 Reorder the terms: 0.25 + x = -1.436140662 Solving 0.25 + x = -1.436140662 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -1.436140662 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -1.436140662 + -0.25 x = -1.436140662 + -0.25 Combine like terms: -1.436140662 + -0.25 = -1.686140662 x = -1.686140662 Simplifying x = -1.686140662

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.186140662, -1.686140662}

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