2x^2-35x+2=0

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Solution for 2x^2-35x+2=0 equation: 


Simplifying
2x2 + -35x + 2 = 0

Reorder the terms:
2 + -35x + 2x2 = 0

Solving
2 + -35x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
1 + -17.5x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -17.5x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -17.5x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -17.5x + x2 = 0 + -1
-17.5x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-17.5x + x2 = -1

The x term is -17.5x.  Take half its coefficient (-8.75).
Square it (76.5625) and add it to both sides.

Add '76.5625' to each side of the equation.
-17.5x + 76.5625 + x2 = -1 + 76.5625

Reorder the terms:
76.5625 + -17.5x + x2 = -1 + 76.5625

Combine like terms: -1 + 76.5625 = 75.5625
76.5625 + -17.5x + x2 = 75.5625

Factor a perfect square on the left side:
(x + -8.75)(x + -8.75) = 75.5625

Calculate the square root of the right side: 8.692669325

Break this problem into two subproblems by setting 
(x + -8.75) equal to 8.692669325 and -8.692669325.


Subproblem 1
x + -8.75 = 8.692669325

Simplifying
x + -8.75 = 8.692669325

Reorder the terms:
-8.75 + x = 8.692669325

Solving
-8.75 + x = 8.692669325

Solving for variable 'x'.

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

Add '8.75' to each side of the equation.
-8.75 + 8.75 + x = 8.692669325 + 8.75

Combine like terms: -8.75 + 8.75 = 0.00
0.00 + x = 8.692669325 + 8.75
x = 8.692669325 + 8.75

Combine like terms: 8.692669325 + 8.75 = 17.442669325
x = 17.442669325

Simplifying
x = 17.442669325


Subproblem 2
x + -8.75 = -8.692669325

Simplifying
x + -8.75 = -8.692669325

Reorder the terms:
-8.75 + x = -8.692669325

Solving
-8.75 + x = -8.692669325

Solving for variable 'x'.

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

Add '8.75' to each side of the equation.
-8.75 + 8.75 + x = -8.692669325 + 8.75

Combine like terms: -8.75 + 8.75 = 0.00
0.00 + x = -8.692669325 + 8.75
x = -8.692669325 + 8.75

Combine like terms: -8.692669325 + 8.75 = 0.057330675
x = 0.057330675

Simplifying
x = 0.057330675


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.442669325, 0.057330675}

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