0=100+96x-16x^2

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Solution for 0=100+96x-16x^2 equation: 


Simplifying
0 = 100 + 96x + -16x2

Solving
0 = 100 + 96x + -16x2

Solving for variable 'x'.

Combine like terms: 0 + -100 = -100
-100 + -96x + 16x2 = 100 + 96x + -16x2 + -100 + -96x + 16x2

Reorder the terms:
-100 + -96x + 16x2 = 100 + -100 + 96x + -96x + -16x2 + 16x2

Combine like terms: 100 + -100 = 0
-100 + -96x + 16x2 = 0 + 96x + -96x + -16x2 + 16x2
-100 + -96x + 16x2 = 96x + -96x + -16x2 + 16x2

Combine like terms: 96x + -96x = 0
-100 + -96x + 16x2 = 0 + -16x2 + 16x2
-100 + -96x + 16x2 = -16x2 + 16x2

Combine like terms: -16x2 + 16x2 = 0
-100 + -96x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-25 + -24x + 4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-25 + -24x + 4x2)' equal to zero and attempt to solve:

Simplifying
-25 + -24x + 4x2 = 0

Solving
-25 + -24x + 4x2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-6.25 + -6x + x2 = 0

Move the constant term to the right:

Add '6.25' to each side of the equation.
-6.25 + -6x + 6.25 + x2 = 0 + 6.25

Reorder the terms:
-6.25 + 6.25 + -6x + x2 = 0 + 6.25

Combine like terms: -6.25 + 6.25 = 0.00
0.00 + -6x + x2 = 0 + 6.25
-6x + x2 = 0 + 6.25

Combine like terms: 0 + 6.25 = 6.25
-6x + x2 = 6.25

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 6.25 + 9

Reorder the terms:
9 + -6x + x2 = 6.25 + 9

Combine like terms: 6.25 + 9 = 15.25
9 + -6x + x2 = 15.25

Factor a perfect square on the left side:
(x + -3)(x + -3) = 15.25

Calculate the square root of the right side: 3.905124838

Break this problem into two subproblems by setting 
(x + -3) equal to 3.905124838 and -3.905124838.


Subproblem 1
x + -3 = 3.905124838

Simplifying
x + -3 = 3.905124838

Reorder the terms:
-3 + x = 3.905124838

Solving
-3 + x = 3.905124838

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = 3.905124838 + 3

Combine like terms: -3 + 3 = 0
0 + x = 3.905124838 + 3
x = 3.905124838 + 3

Combine like terms: 3.905124838 + 3 = 6.905124838
x = 6.905124838

Simplifying
x = 6.905124838


Subproblem 2
x + -3 = -3.905124838

Simplifying
x + -3 = -3.905124838

Reorder the terms:
-3 + x = -3.905124838

Solving
-3 + x = -3.905124838

Solving for variable 'x'.

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

Add '3' to each side of the equation.
-3 + 3 + x = -3.905124838 + 3

Combine like terms: -3 + 3 = 0
0 + x = -3.905124838 + 3
x = -3.905124838 + 3

Combine like terms: -3.905124838 + 3 = -0.905124838
x = -0.905124838

Simplifying
x = -0.905124838


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.905124838, -0.905124838}
Solution
x = {6.905124838, -0.905124838}

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