-16x^2+75x-51=0

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Solution for -16x^2+75x-51=0 equation: 


Simplifying
-16x2 + 75x + -51 = 0

Reorder the terms:
-51 + 75x + -16x2 = 0

Solving
-51 + 75x + -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'.
3.1875 + -4.6875x + x2 = 0

Move the constant term to the right:

Add '-3.1875' to each side of the equation.
3.1875 + -4.6875x + -3.1875 + x2 = 0 + -3.1875

Reorder the terms:
3.1875 + -3.1875 + -4.6875x + x2 = 0 + -3.1875

Combine like terms: 3.1875 + -3.1875 = 0.0000
0.0000 + -4.6875x + x2 = 0 + -3.1875
-4.6875x + x2 = 0 + -3.1875

Combine like terms: 0 + -3.1875 = -3.1875
-4.6875x + x2 = -3.1875

The x term is -4.6875x.  Take half its coefficient (-2.34375).
Square it (5.493164063) and add it to both sides.

Add '5.493164063' to each side of the equation.
-4.6875x + 5.493164063 + x2 = -3.1875 + 5.493164063

Reorder the terms:
5.493164063 + -4.6875x + x2 = -3.1875 + 5.493164063

Combine like terms: -3.1875 + 5.493164063 = 2.305664063
5.493164063 + -4.6875x + x2 = 2.305664063

Factor a perfect square on the left side:
(x + -2.34375)(x + -2.34375) = 2.305664063

Calculate the square root of the right side: 1.518441327

Break this problem into two subproblems by setting 
(x + -2.34375) equal to 1.518441327 and -1.518441327.


Subproblem 1
x + -2.34375 = 1.518441327

Simplifying
x + -2.34375 = 1.518441327

Reorder the terms:
-2.34375 + x = 1.518441327

Solving
-2.34375 + x = 1.518441327

Solving for variable 'x'.

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

Add '2.34375' to each side of the equation.
-2.34375 + 2.34375 + x = 1.518441327 + 2.34375

Combine like terms: -2.34375 + 2.34375 = 0.00000
0.00000 + x = 1.518441327 + 2.34375
x = 1.518441327 + 2.34375

Combine like terms: 1.518441327 + 2.34375 = 3.862191327
x = 3.862191327

Simplifying
x = 3.862191327


Subproblem 2
x + -2.34375 = -1.518441327

Simplifying
x + -2.34375 = -1.518441327

Reorder the terms:
-2.34375 + x = -1.518441327

Solving
-2.34375 + x = -1.518441327

Solving for variable 'x'.

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

Add '2.34375' to each side of the equation.
-2.34375 + 2.34375 + x = -1.518441327 + 2.34375

Combine like terms: -2.34375 + 2.34375 = 0.00000
0.00000 + x = -1.518441327 + 2.34375
x = -1.518441327 + 2.34375

Combine like terms: -1.518441327 + 2.34375 = 0.825308673
x = 0.825308673

Simplifying
x = 0.825308673


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.862191327, 0.825308673}

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