-16x^2+105x-34=

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


Simplifying
-16x2 + 105x + -34 = 0

Reorder the terms:
-34 + 105x + -16x2 = 0

Solving
-34 + 105x + -16x2 = 0

Solving for variable 'x'.

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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