2x*x+x=32

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Solution for 2x*x+x=32 equation: 


Simplifying
2x * x + x = 32

Multiply x * x
2x2 + x = 32

Reorder the terms:
x + 2x2 = 32

Solving
x + 2x2 = 32

Solving for variable 'x'.

Reorder the terms:
-32 + x + 2x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-32 + x + 2x2 = 0

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

Divide each side by '2'.
-16 + 0.5x + x2 = 0

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + 0.5x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + 0.5x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + 0.5x + x2 = 0 + 16
0.5x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
0.5x + x2 = 16

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.
0.5x + 0.25 + x2 = 16 + 0.25

Reorder the terms:
0.25 + 0.5x + x2 = 16 + 0.25

Combine like terms: 16 + 0.25 = 16.25
0.25 + 0.5x + x2 = 16.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 16.25

Calculate the square root of the right side: 4.031128874

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.031128874 and -4.031128874.


Subproblem 1
x + 0.5 = 4.031128874

Simplifying
x + 0.5 = 4.031128874

Reorder the terms:
0.5 + x = 4.031128874

Solving
0.5 + x = 4.031128874

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 = 4.031128874 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 4.031128874 + -0.5
x = 4.031128874 + -0.5

Combine like terms: 4.031128874 + -0.5 = 3.531128874
x = 3.531128874

Simplifying
x = 3.531128874


Subproblem 2
x + 0.5 = -4.031128874

Simplifying
x + 0.5 = -4.031128874

Reorder the terms:
0.5 + x = -4.031128874

Solving
0.5 + x = -4.031128874

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 = -4.031128874 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -4.031128874 + -0.5
x = -4.031128874 + -0.5

Combine like terms: -4.031128874 + -0.5 = -4.531128874
x = -4.531128874

Simplifying
x = -4.531128874


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.531128874, -4.531128874}

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