-16x^2+30x+3.5=0

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Solution for -16x^2+30x+3.5=0 equation: 


Simplifying
-16x2 + 30x + 3.5 = 0

Reorder the terms:
3.5 + 30x + -16x2 = 0

Solving
3.5 + 30x + -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 + -1.875x + x2 = 0

Move the constant term to the right:

Add '0.21875' to each side of the equation.
-0.21875 + -1.875x + 0.21875 + x2 = 0 + 0.21875

Reorder the terms:
-0.21875 + 0.21875 + -1.875x + x2 = 0 + 0.21875

Combine like terms: -0.21875 + 0.21875 = 0.00000
0.00000 + -1.875x + x2 = 0 + 0.21875
-1.875x + x2 = 0 + 0.21875

Combine like terms: 0 + 0.21875 = 0.21875
-1.875x + x2 = 0.21875

The x term is -1.875x.  Take half its coefficient (-0.9375).
Square it (0.87890625) and add it to both sides.

Add '0.87890625' to each side of the equation.
-1.875x + 0.87890625 + x2 = 0.21875 + 0.87890625

Reorder the terms:
0.87890625 + -1.875x + x2 = 0.21875 + 0.87890625

Combine like terms: 0.21875 + 0.87890625 = 1.09765625
0.87890625 + -1.875x + x2 = 1.09765625

Factor a perfect square on the left side:
(x + -0.9375)(x + -0.9375) = 1.09765625

Calculate the square root of the right side: 1.047690913

Break this problem into two subproblems by setting 
(x + -0.9375) equal to 1.047690913 and -1.047690913.


Subproblem 1
x + -0.9375 = 1.047690913

Simplifying
x + -0.9375 = 1.047690913

Reorder the terms:
-0.9375 + x = 1.047690913

Solving
-0.9375 + x = 1.047690913

Solving for variable 'x'.

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

Add '0.9375' to each side of the equation.
-0.9375 + 0.9375 + x = 1.047690913 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + x = 1.047690913 + 0.9375
x = 1.047690913 + 0.9375

Combine like terms: 1.047690913 + 0.9375 = 1.985190913
x = 1.985190913

Simplifying
x = 1.985190913


Subproblem 2
x + -0.9375 = -1.047690913

Simplifying
x + -0.9375 = -1.047690913

Reorder the terms:
-0.9375 + x = -1.047690913

Solving
-0.9375 + x = -1.047690913

Solving for variable 'x'.

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

Add '0.9375' to each side of the equation.
-0.9375 + 0.9375 + x = -1.047690913 + 0.9375

Combine like terms: -0.9375 + 0.9375 = 0.0000
0.0000 + x = -1.047690913 + 0.9375
x = -1.047690913 + 0.9375

Combine like terms: -1.047690913 + 0.9375 = -0.110190913
x = -0.110190913

Simplifying
x = -0.110190913


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.985190913, -0.110190913}

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