X^2-3.508X+2.339=0

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Solution for X^2-3.508X+2.339=0 equation: 


Simplifying
X2 + -3.508X + 2.339 = 0

Reorder the terms:
2.339 + -3.508X + X2 = 0

Solving
2.339 + -3.508X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '-2.339' to each side of the equation.
2.339 + -3.508X + -2.339 + X2 = 0 + -2.339

Reorder the terms:
2.339 + -2.339 + -3.508X + X2 = 0 + -2.339

Combine like terms: 2.339 + -2.339 = 0.000
0.000 + -3.508X + X2 = 0 + -2.339
-3.508X + X2 = 0 + -2.339

Combine like terms: 0 + -2.339 = -2.339
-3.508X + X2 = -2.339

The X term is -3.508X.  Take half its coefficient (-1.754).
Square it (3.076516) and add it to both sides.

Add '3.076516' to each side of the equation.
-3.508X + 3.076516 + X2 = -2.339 + 3.076516

Reorder the terms:
3.076516 + -3.508X + X2 = -2.339 + 3.076516

Combine like terms: -2.339 + 3.076516 = 0.737516
3.076516 + -3.508X + X2 = 0.737516

Factor a perfect square on the left side:
(X + -1.754)(X + -1.754) = 0.737516

Calculate the square root of the right side: 0.858787517

Break this problem into two subproblems by setting 
(X + -1.754) equal to 0.858787517 and -0.858787517.


Subproblem 1
X + -1.754 = 0.858787517

Simplifying
X + -1.754 = 0.858787517

Reorder the terms:
-1.754 + X = 0.858787517

Solving
-1.754 + X = 0.858787517

Solving for variable 'X'.

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

Add '1.754' to each side of the equation.
-1.754 + 1.754 + X = 0.858787517 + 1.754

Combine like terms: -1.754 + 1.754 = 0.000
0.000 + X = 0.858787517 + 1.754
X = 0.858787517 + 1.754

Combine like terms: 0.858787517 + 1.754 = 2.612787517
X = 2.612787517

Simplifying
X = 2.612787517


Subproblem 2
X + -1.754 = -0.858787517

Simplifying
X + -1.754 = -0.858787517

Reorder the terms:
-1.754 + X = -0.858787517

Solving
-1.754 + X = -0.858787517

Solving for variable 'X'.

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

Add '1.754' to each side of the equation.
-1.754 + 1.754 + X = -0.858787517 + 1.754

Combine like terms: -1.754 + 1.754 = 0.000
0.000 + X = -0.858787517 + 1.754
X = -0.858787517 + 1.754

Combine like terms: -0.858787517 + 1.754 = 0.895212483
X = 0.895212483

Simplifying
X = 0.895212483


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {2.612787517, 0.895212483}

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