-16x^2+65x-46.5=0

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Solution for -16x^2+65x-46.5=0 equation: 


Simplifying
-16x2 + 65x + -46.5 = 0

Reorder the terms:
-46.5 + 65x + -16x2 = 0

Solving
-46.5 + 65x + -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'.
2.90625 + -4.0625x + x2 = 0

Move the constant term to the right:

Add '-2.90625' to each side of the equation.
2.90625 + -4.0625x + -2.90625 + x2 = 0 + -2.90625

Reorder the terms:
2.90625 + -2.90625 + -4.0625x + x2 = 0 + -2.90625

Combine like terms: 2.90625 + -2.90625 = 0.00000
0.00000 + -4.0625x + x2 = 0 + -2.90625
-4.0625x + x2 = 0 + -2.90625

Combine like terms: 0 + -2.90625 = -2.90625
-4.0625x + x2 = -2.90625

The x term is -4.0625x.  Take half its coefficient (-2.03125).
Square it (4.125976563) and add it to both sides.

Add '4.125976563' to each side of the equation.
-4.0625x + 4.125976563 + x2 = -2.90625 + 4.125976563

Reorder the terms:
4.125976563 + -4.0625x + x2 = -2.90625 + 4.125976563

Combine like terms: -2.90625 + 4.125976563 = 1.219726563
4.125976563 + -4.0625x + x2 = 1.219726563

Factor a perfect square on the left side:
(x + -2.03125)(x + -2.03125) = 1.219726563

Calculate the square root of the right side: 1.104412316

Break this problem into two subproblems by setting 
(x + -2.03125) equal to 1.104412316 and -1.104412316.


Subproblem 1
x + -2.03125 = 1.104412316

Simplifying
x + -2.03125 = 1.104412316

Reorder the terms:
-2.03125 + x = 1.104412316

Solving
-2.03125 + x = 1.104412316

Solving for variable 'x'.

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

Add '2.03125' to each side of the equation.
-2.03125 + 2.03125 + x = 1.104412316 + 2.03125

Combine like terms: -2.03125 + 2.03125 = 0.00000
0.00000 + x = 1.104412316 + 2.03125
x = 1.104412316 + 2.03125

Combine like terms: 1.104412316 + 2.03125 = 3.135662316
x = 3.135662316

Simplifying
x = 3.135662316


Subproblem 2
x + -2.03125 = -1.104412316

Simplifying
x + -2.03125 = -1.104412316

Reorder the terms:
-2.03125 + x = -1.104412316

Solving
-2.03125 + x = -1.104412316

Solving for variable 'x'.

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

Add '2.03125' to each side of the equation.
-2.03125 + 2.03125 + x = -1.104412316 + 2.03125

Combine like terms: -2.03125 + 2.03125 = 0.00000
0.00000 + x = -1.104412316 + 2.03125
x = -1.104412316 + 2.03125

Combine like terms: -1.104412316 + 2.03125 = 0.926837684
x = 0.926837684

Simplifying
x = 0.926837684


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.135662316, 0.926837684}

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