105x-16x^2=34

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Solution for 105x-16x^2=34 equation: 


Simplifying
105x + -16x2 = 34

Solving
105x + -16x2 = 34

Solving for variable 'x'.

Reorder the terms:
-34 + 105x + -16x2 = 34 + -34

Combine like terms: 34 + -34 = 0
-34 + 105x + -16x2 = 0

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
2.125 + -6.5625x + x2 = 0

Move the constant term to the right:

Add '-2.125' to each side of the equation.
2.125 + -6.5625x + -2.125 + x2 = 0 + -2.125

Reorder the terms:
2.125 + -2.125 + -6.5625x + x2 = 0 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + -6.5625x + x2 = 0 + -2.125
-6.5625x + x2 = 0 + -2.125

Combine like terms: 0 + -2.125 = -2.125
-6.5625x + x2 = -2.125

The x term is -6.5625x.  Take half its coefficient (-3.28125).
Square it (10.76660156) and add it to both sides.

Add '10.76660156' to each side of the equation.
-6.5625x + 10.76660156 + x2 = -2.125 + 10.76660156

Reorder the terms:
10.76660156 + -6.5625x + x2 = -2.125 + 10.76660156

Combine like terms: -2.125 + 10.76660156 = 8.64160156
10.76660156 + -6.5625x + x2 = 8.64160156

Factor a perfect square on the left side:
(x + -3.28125)(x + -3.28125) = 8.64160156

Calculate the square root of the right side: 2.93966011

Break this problem into two subproblems by setting 
(x + -3.28125) equal to 2.93966011 and -2.93966011.


Subproblem 1
x + -3.28125 = 2.93966011

Simplifying
x + -3.28125 = 2.93966011

Reorder the terms:
-3.28125 + x = 2.93966011

Solving
-3.28125 + x = 2.93966011

Solving for variable 'x'.

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

Add '3.28125' to each side of the equation.
-3.28125 + 3.28125 + x = 2.93966011 + 3.28125

Combine like terms: -3.28125 + 3.28125 = 0.00000
0.00000 + x = 2.93966011 + 3.28125
x = 2.93966011 + 3.28125

Combine like terms: 2.93966011 + 3.28125 = 6.22091011
x = 6.22091011

Simplifying
x = 6.22091011


Subproblem 2
x + -3.28125 = -2.93966011

Simplifying
x + -3.28125 = -2.93966011

Reorder the terms:
-3.28125 + x = -2.93966011

Solving
-3.28125 + x = -2.93966011

Solving for variable 'x'.

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

Add '3.28125' to each side of the equation.
-3.28125 + 3.28125 + x = -2.93966011 + 3.28125

Combine like terms: -3.28125 + 3.28125 = 0.00000
0.00000 + x = -2.93966011 + 3.28125
x = -2.93966011 + 3.28125

Combine like terms: -2.93966011 + 3.28125 = 0.34158989
x = 0.34158989

Simplifying
x = 0.34158989


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.22091011, 0.34158989}

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