-16x^2+65x+8=0

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Solution for -16x^2+65x+8=0 equation: 


Simplifying
-16x2 + 65x + 8 = 0

Reorder the terms:
8 + 65x + -16x2 = 0

Solving
8 + 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'.
-0.5 + -4.0625x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -4.0625x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -4.0625x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -4.0625x + x2 = 0 + 0.5
-4.0625x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-4.0625x + x2 = 0.5

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 = 0.5 + 4.125976563

Reorder the terms:
4.125976563 + -4.0625x + x2 = 0.5 + 4.125976563

Combine like terms: 0.5 + 4.125976563 = 4.625976563
4.125976563 + -4.0625x + x2 = 4.625976563

Factor a perfect square on the left side:
(x + -2.03125)(x + -2.03125) = 4.625976563

Calculate the square root of the right side: 2.150808351

Break this problem into two subproblems by setting 
(x + -2.03125) equal to 2.150808351 and -2.150808351.


Subproblem 1
x + -2.03125 = 2.150808351

Simplifying
x + -2.03125 = 2.150808351

Reorder the terms:
-2.03125 + x = 2.150808351

Solving
-2.03125 + x = 2.150808351

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 = 2.150808351 + 2.03125

Combine like terms: -2.03125 + 2.03125 = 0.00000
0.00000 + x = 2.150808351 + 2.03125
x = 2.150808351 + 2.03125

Combine like terms: 2.150808351 + 2.03125 = 4.182058351
x = 4.182058351

Simplifying
x = 4.182058351


Subproblem 2
x + -2.03125 = -2.150808351

Simplifying
x + -2.03125 = -2.150808351

Reorder the terms:
-2.03125 + x = -2.150808351

Solving
-2.03125 + x = -2.150808351

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 = -2.150808351 + 2.03125

Combine like terms: -2.03125 + 2.03125 = 0.00000
0.00000 + x = -2.150808351 + 2.03125
x = -2.150808351 + 2.03125

Combine like terms: -2.150808351 + 2.03125 = -0.119558351
x = -0.119558351

Simplifying
x = -0.119558351


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.182058351, -0.119558351}

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