-1.04x^2+20x-96=0

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Solution for -1.04x^2+20x-96=0 equation: 


Simplifying
-1.04x2 + 20x + -96 = 0

Reorder the terms:
-96 + 20x + -1.04x2 = 0

Solving
-96 + 20x + -1.04x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1.04 the coefficient of the squared term: 

Divide each side by '-1.04'.
92.30769231 + -19.23076923x + x2 = 0

Move the constant term to the right:

Add '-92.30769231' to each side of the equation.
92.30769231 + -19.23076923x + -92.30769231 + x2 = 0 + -92.30769231

Reorder the terms:
92.30769231 + -92.30769231 + -19.23076923x + x2 = 0 + -92.30769231

Combine like terms: 92.30769231 + -92.30769231 = 0.00000000
0.00000000 + -19.23076923x + x2 = 0 + -92.30769231
-19.23076923x + x2 = 0 + -92.30769231

Combine like terms: 0 + -92.30769231 = -92.30769231
-19.23076923x + x2 = -92.30769231

The x term is -19.23076923x.  Take half its coefficient (-9.615384615).
Square it (92.45562129) and add it to both sides.

Add '92.45562129' to each side of the equation.
-19.23076923x + 92.45562129 + x2 = -92.30769231 + 92.45562129

Reorder the terms:
92.45562129 + -19.23076923x + x2 = -92.30769231 + 92.45562129

Combine like terms: -92.30769231 + 92.45562129 = 0.14792898
92.45562129 + -19.23076923x + x2 = 0.14792898

Factor a perfect square on the left side:
(x + -9.615384615)(x + -9.615384615) = 0.14792898

Calculate the square root of the right side: 0.384615366

Break this problem into two subproblems by setting 
(x + -9.615384615) equal to 0.384615366 and -0.384615366.


Subproblem 1
x + -9.615384615 = 0.384615366

Simplifying
x + -9.615384615 = 0.384615366

Reorder the terms:
-9.615384615 + x = 0.384615366

Solving
-9.615384615 + x = 0.384615366

Solving for variable 'x'.

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

Add '9.615384615' to each side of the equation.
-9.615384615 + 9.615384615 + x = 0.384615366 + 9.615384615

Combine like terms: -9.615384615 + 9.615384615 = 0.000000000
0.000000000 + x = 0.384615366 + 9.615384615
x = 0.384615366 + 9.615384615

Combine like terms: 0.384615366 + 9.615384615 = 9.999999981
x = 9.999999981

Simplifying
x = 9.999999981


Subproblem 2
x + -9.615384615 = -0.384615366

Simplifying
x + -9.615384615 = -0.384615366

Reorder the terms:
-9.615384615 + x = -0.384615366

Solving
-9.615384615 + x = -0.384615366

Solving for variable 'x'.

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

Add '9.615384615' to each side of the equation.
-9.615384615 + 9.615384615 + x = -0.384615366 + 9.615384615

Combine like terms: -9.615384615 + 9.615384615 = 0.000000000
0.000000000 + x = -0.384615366 + 9.615384615
x = -0.384615366 + 9.615384615

Combine like terms: -0.384615366 + 9.615384615 = 9.230769249
x = 9.230769249

Simplifying
x = 9.230769249


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.999999981, 9.230769249}

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