-16x^2+94x+3.5=0

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Solution for -16x^2+94x+3.5=0 equation: 


Simplifying
-16x2 + 94x + 3.5 = 0

Reorder the terms:
3.5 + 94x + -16x2 = 0

Solving
3.5 + 94x + -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'.
-0.21875 + -5.875x + x2 = 0

Move the constant term to the right:

Add '0.21875' to each side of the equation.
-0.21875 + -5.875x + 0.21875 + x2 = 0 + 0.21875

Reorder the terms:
-0.21875 + 0.21875 + -5.875x + x2 = 0 + 0.21875

Combine like terms: -0.21875 + 0.21875 = 0.00000
0.00000 + -5.875x + x2 = 0 + 0.21875
-5.875x + x2 = 0 + 0.21875

Combine like terms: 0 + 0.21875 = 0.21875
-5.875x + x2 = 0.21875

The x term is -5.875x.  Take half its coefficient (-2.9375).
Square it (8.62890625) and add it to both sides.

Add '8.62890625' to each side of the equation.
-5.875x + 8.62890625 + x2 = 0.21875 + 8.62890625

Reorder the terms:
8.62890625 + -5.875x + x2 = 0.21875 + 8.62890625

Combine like terms: 0.21875 + 8.62890625 = 8.84765625
8.62890625 + -5.875x + x2 = 8.84765625

Factor a perfect square on the left side:
(x + -2.9375)(x + -2.9375) = 8.84765625

Calculate the square root of the right side: 2.974501009

Break this problem into two subproblems by setting 
(x + -2.9375) equal to 2.974501009 and -2.974501009.


Subproblem 1
x + -2.9375 = 2.974501009

Simplifying
x + -2.9375 = 2.974501009

Reorder the terms:
-2.9375 + x = 2.974501009

Solving
-2.9375 + x = 2.974501009

Solving for variable 'x'.

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

Add '2.9375' to each side of the equation.
-2.9375 + 2.9375 + x = 2.974501009 + 2.9375

Combine like terms: -2.9375 + 2.9375 = 0.0000
0.0000 + x = 2.974501009 + 2.9375
x = 2.974501009 + 2.9375

Combine like terms: 2.974501009 + 2.9375 = 5.912001009
x = 5.912001009

Simplifying
x = 5.912001009


Subproblem 2
x + -2.9375 = -2.974501009

Simplifying
x + -2.9375 = -2.974501009

Reorder the terms:
-2.9375 + x = -2.974501009

Solving
-2.9375 + x = -2.974501009

Solving for variable 'x'.

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

Add '2.9375' to each side of the equation.
-2.9375 + 2.9375 + x = -2.974501009 + 2.9375

Combine like terms: -2.9375 + 2.9375 = 0.0000
0.0000 + x = -2.974501009 + 2.9375
x = -2.974501009 + 2.9375

Combine like terms: -2.974501009 + 2.9375 = -0.037001009
x = -0.037001009

Simplifying
x = -0.037001009


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.912001009, -0.037001009}

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