x^2-39x+2=0

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Solution for x^2-39x+2=0 equation:


Simplifying
x2 + -39x + 2 = 0

Reorder the terms:
2 + -39x + x2 = 0

Solving
2 + -39x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -39x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -39x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -39x + x2 = 0 + -2
-39x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
-39x + x2 = -2

The x term is -39x.  Take half its coefficient (-19.5).
Square it (380.25) and add it to both sides.

Add '380.25' to each side of the equation.
-39x + 380.25 + x2 = -2 + 380.25

Reorder the terms:
380.25 + -39x + x2 = -2 + 380.25

Combine like terms: -2 + 380.25 = 378.25
380.25 + -39x + x2 = 378.25

Factor a perfect square on the left side:
(x + -19.5)(x + -19.5) = 378.25

Calculate the square root of the right side: 19.448650339

Break this problem into two subproblems by setting 
(x + -19.5) equal to 19.448650339 and -19.448650339.

Subproblem 1

x + -19.5 = 19.448650339 Simplifying x + -19.5 = 19.448650339 Reorder the terms: -19.5 + x = 19.448650339 Solving -19.5 + x = 19.448650339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.5' to each side of the equation. -19.5 + 19.5 + x = 19.448650339 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x = 19.448650339 + 19.5 x = 19.448650339 + 19.5 Combine like terms: 19.448650339 + 19.5 = 38.948650339 x = 38.948650339 Simplifying x = 38.948650339

Subproblem 2

x + -19.5 = -19.448650339 Simplifying x + -19.5 = -19.448650339 Reorder the terms: -19.5 + x = -19.448650339 Solving -19.5 + x = -19.448650339 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.5' to each side of the equation. -19.5 + 19.5 + x = -19.448650339 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x = -19.448650339 + 19.5 x = -19.448650339 + 19.5 Combine like terms: -19.448650339 + 19.5 = 0.051349661 x = 0.051349661 Simplifying x = 0.051349661

Solution

The solution to the problem is based on the solutions from the subproblems. x = {38.948650339, 0.051349661}

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