4x^2-33x+64=0

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Solution for 4x^2-33x+64=0 equation: 


Simplifying
4x2 + -33x + 64 = 0

Reorder the terms:
64 + -33x + 4x2 = 0

Solving
64 + -33x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
16 + -8.25x + x2 = 0

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -8.25x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -8.25x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -8.25x + x2 = 0 + -16
-8.25x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-8.25x + x2 = -16

The x term is -8.25x.  Take half its coefficient (-4.125).
Square it (17.015625) and add it to both sides.

Add '17.015625' to each side of the equation.
-8.25x + 17.015625 + x2 = -16 + 17.015625

Reorder the terms:
17.015625 + -8.25x + x2 = -16 + 17.015625

Combine like terms: -16 + 17.015625 = 1.015625
17.015625 + -8.25x + x2 = 1.015625

Factor a perfect square on the left side:
(x + -4.125)(x + -4.125) = 1.015625

Calculate the square root of the right side: 1.007782219

Break this problem into two subproblems by setting 
(x + -4.125) equal to 1.007782219 and -1.007782219.


Subproblem 1
x + -4.125 = 1.007782219

Simplifying
x + -4.125 = 1.007782219

Reorder the terms:
-4.125 + x = 1.007782219

Solving
-4.125 + x = 1.007782219

Solving for variable 'x'.

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

Add '4.125' to each side of the equation.
-4.125 + 4.125 + x = 1.007782219 + 4.125

Combine like terms: -4.125 + 4.125 = 0.000
0.000 + x = 1.007782219 + 4.125
x = 1.007782219 + 4.125

Combine like terms: 1.007782219 + 4.125 = 5.132782219
x = 5.132782219

Simplifying
x = 5.132782219


Subproblem 2
x + -4.125 = -1.007782219

Simplifying
x + -4.125 = -1.007782219

Reorder the terms:
-4.125 + x = -1.007782219

Solving
-4.125 + x = -1.007782219

Solving for variable 'x'.

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

Add '4.125' to each side of the equation.
-4.125 + 4.125 + x = -1.007782219 + 4.125

Combine like terms: -4.125 + 4.125 = 0.000
0.000 + x = -1.007782219 + 4.125
x = -1.007782219 + 4.125

Combine like terms: -1.007782219 + 4.125 = 3.117217781
x = 3.117217781

Simplifying
x = 3.117217781


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.132782219, 3.117217781}

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