x^2-9.6x=1.96

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Solution for x^2-9.6x=1.96 equation: 


Simplifying
x2 + -9.6x = 1.96

Reorder the terms:
-9.6x + x2 = 1.96

Solving
-9.6x + x2 = 1.96

Solving for variable 'x'.

Reorder the terms:
-1.96 + -9.6x + x2 = 1.96 + -1.96

Combine like terms: 1.96 + -1.96 = 0.00
-1.96 + -9.6x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '1.96' to each side of the equation.
-1.96 + -9.6x + 1.96 + x2 = 0.00 + 1.96

Reorder the terms:
-1.96 + 1.96 + -9.6x + x2 = 0.00 + 1.96

Combine like terms: -1.96 + 1.96 = 0.00
0.00 + -9.6x + x2 = 0.00 + 1.96
-9.6x + x2 = 0.00 + 1.96

Combine like terms: 0.00 + 1.96 = 1.96
-9.6x + x2 = 1.96

The x term is -9.6x.  Take half its coefficient (-4.8).
Square it (23.04) and add it to both sides.

Add '23.04' to each side of the equation.
-9.6x + 23.04 + x2 = 1.96 + 23.04

Reorder the terms:
23.04 + -9.6x + x2 = 1.96 + 23.04

Combine like terms: 1.96 + 23.04 = 25
23.04 + -9.6x + x2 = 25

Factor a perfect square on the left side:
(x + -4.8)(x + -4.8) = 25

Calculate the square root of the right side: 5

Break this problem into two subproblems by setting 
(x + -4.8) equal to 5 and -5.


Subproblem 1
x + -4.8 = 5

Simplifying
x + -4.8 = 5

Reorder the terms:
-4.8 + x = 5

Solving
-4.8 + x = 5

Solving for variable 'x'.

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

Add '4.8' to each side of the equation.
-4.8 + 4.8 + x = 5 + 4.8

Combine like terms: -4.8 + 4.8 = 0.0
0.0 + x = 5 + 4.8
x = 5 + 4.8

Combine like terms: 5 + 4.8 = 9.8
x = 9.8

Simplifying
x = 9.8


Subproblem 2
x + -4.8 = -5

Simplifying
x + -4.8 = -5

Reorder the terms:
-4.8 + x = -5

Solving
-4.8 + x = -5

Solving for variable 'x'.

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

Add '4.8' to each side of the equation.
-4.8 + 4.8 + x = -5 + 4.8

Combine like terms: -4.8 + 4.8 = 0.0
0.0 + x = -5 + 4.8
x = -5 + 4.8

Combine like terms: -5 + 4.8 = -0.2
x = -0.2

Simplifying
x = -0.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.8, -0.2}

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