-16x^2+75x-50=0

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Solution for -16x^2+75x-50=0 equation:


Simplifying
-16x2 + 75x + -50 = 0

Reorder the terms:
-50 + 75x + -16x2 = 0

Solving
-50 + 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'.
3.125 + -4.6875x + x2 = 0

Move the constant term to the right:

Add '-3.125' to each side of the equation.
3.125 + -4.6875x + -3.125 + x2 = 0 + -3.125

Reorder the terms:
3.125 + -3.125 + -4.6875x + x2 = 0 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + -4.6875x + x2 = 0 + -3.125
-4.6875x + x2 = 0 + -3.125

Combine like terms: 0 + -3.125 = -3.125
-4.6875x + x2 = -3.125

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 = -3.125 + 5.493164063

Reorder the terms:
5.493164063 + -4.6875x + x2 = -3.125 + 5.493164063

Combine like terms: -3.125 + 5.493164063 = 2.368164063
5.493164063 + -4.6875x + x2 = 2.368164063

Factor a perfect square on the left side:
(x + -2.34375)(x + -2.34375) = 2.368164063

Calculate the square root of the right side: 1.538884032

Break this problem into two subproblems by setting 
(x + -2.34375) equal to 1.538884032 and -1.538884032.


Subproblem 1
x + -2.34375 = 1.538884032

Simplifying
x + -2.34375 = 1.538884032

Reorder the terms:
-2.34375 + x = 1.538884032

Solving
-2.34375 + x = 1.538884032

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 = 1.538884032 + 2.34375

Combine like terms: -2.34375 + 2.34375 = 0.00000
0.00000 + x = 1.538884032 + 2.34375
x = 1.538884032 + 2.34375

Combine like terms: 1.538884032 + 2.34375 = 3.882634032
x = 3.882634032

Simplifying
x = 3.882634032


Subproblem 2
x + -2.34375 = -1.538884032

Simplifying
x + -2.34375 = -1.538884032

Reorder the terms:
-2.34375 + x = -1.538884032

Solving
-2.34375 + x = -1.538884032

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 = -1.538884032 + 2.34375

Combine like terms: -2.34375 + 2.34375 = 0.00000
0.00000 + x = -1.538884032 + 2.34375
x = -1.538884032 + 2.34375

Combine like terms: -1.538884032 + 2.34375 = 0.804865968
x = 0.804865968

Simplifying
x = 0.804865968


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.882634032, 0.804865968}

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