2x^2-59x+64=0

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Solution for 2x^2-59x+64=0 equation: 


Simplifying
2x2 + -59x + 64 = 0

Reorder the terms:
64 + -59x + 2x2 = 0

Solving
64 + -59x + 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'.
32 + -29.5x + x2 = 0

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + -29.5x + -32 + x2 = 0 + -32

Reorder the terms:
32 + -32 + -29.5x + x2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -29.5x + x2 = 0 + -32
-29.5x + x2 = 0 + -32

Combine like terms: 0 + -32 = -32
-29.5x + x2 = -32

The x term is -29.5x.  Take half its coefficient (-14.75).
Square it (217.5625) and add it to both sides.

Add '217.5625' to each side of the equation.
-29.5x + 217.5625 + x2 = -32 + 217.5625

Reorder the terms:
217.5625 + -29.5x + x2 = -32 + 217.5625

Combine like terms: -32 + 217.5625 = 185.5625
217.5625 + -29.5x + x2 = 185.5625

Factor a perfect square on the left side:
(x + -14.75)(x + -14.75) = 185.5625

Calculate the square root of the right side: 13.622132726

Break this problem into two subproblems by setting 
(x + -14.75) equal to 13.622132726 and -13.622132726.


Subproblem 1
x + -14.75 = 13.622132726

Simplifying
x + -14.75 = 13.622132726

Reorder the terms:
-14.75 + x = 13.622132726

Solving
-14.75 + x = 13.622132726

Solving for variable 'x'.

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

Add '14.75' to each side of the equation.
-14.75 + 14.75 + x = 13.622132726 + 14.75

Combine like terms: -14.75 + 14.75 = 0.00
0.00 + x = 13.622132726 + 14.75
x = 13.622132726 + 14.75

Combine like terms: 13.622132726 + 14.75 = 28.372132726
x = 28.372132726

Simplifying
x = 28.372132726


Subproblem 2
x + -14.75 = -13.622132726

Simplifying
x + -14.75 = -13.622132726

Reorder the terms:
-14.75 + x = -13.622132726

Solving
-14.75 + x = -13.622132726

Solving for variable 'x'.

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

Add '14.75' to each side of the equation.
-14.75 + 14.75 + x = -13.622132726 + 14.75

Combine like terms: -14.75 + 14.75 = 0.00
0.00 + x = -13.622132726 + 14.75
x = -13.622132726 + 14.75

Combine like terms: -13.622132726 + 14.75 = 1.127867274
x = 1.127867274

Simplifying
x = 1.127867274


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {28.372132726, 1.127867274}

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