3x^2-4.4x=9.6

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Solution for 3x^2-4.4x=9.6 equation:


Simplifying
3x2 + -4.4x = 9.6

Reorder the terms:
-4.4x + 3x2 = 9.6

Solving
-4.4x + 3x2 = 9.6

Solving for variable 'x'.

Reorder the terms:
-9.6 + -4.4x + 3x2 = 9.6 + -9.6

Combine like terms: 9.6 + -9.6 = 0.0
-9.6 + -4.4x + 3x2 = 0.0

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

Divide each side by '3'.
-3.2 + -1.466666667x + x2 = 0.0

Move the constant term to the right:

Add '3.2' to each side of the equation.
-3.2 + -1.466666667x + 3.2 + x2 = 0.0 + 3.2

Reorder the terms:
-3.2 + 3.2 + -1.466666667x + x2 = 0.0 + 3.2

Combine like terms: -3.2 + 3.2 = 0.0
0.0 + -1.466666667x + x2 = 0.0 + 3.2
-1.466666667x + x2 = 0.0 + 3.2

Combine like terms: 0.0 + 3.2 = 3.2
-1.466666667x + x2 = 3.2

The x term is -1.466666667x.  Take half its coefficient (-0.7333333335).
Square it (0.5377777780) and add it to both sides.

Add '0.5377777780' to each side of the equation.
-1.466666667x + 0.5377777780 + x2 = 3.2 + 0.5377777780

Reorder the terms:
0.5377777780 + -1.466666667x + x2 = 3.2 + 0.5377777780

Combine like terms: 3.2 + 0.5377777780 = 3.737777778
0.5377777780 + -1.466666667x + x2 = 3.737777778

Factor a perfect square on the left side:
(x + -0.7333333335)(x + -0.7333333335) = 3.737777778

Calculate the square root of the right side: 1.933333333

Break this problem into two subproblems by setting 
(x + -0.7333333335) equal to 1.933333333 and -1.933333333.

Subproblem 1

x + -0.7333333335 = 1.933333333 Simplifying x + -0.7333333335 = 1.933333333 Reorder the terms: -0.7333333335 + x = 1.933333333 Solving -0.7333333335 + x = 1.933333333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7333333335' to each side of the equation. -0.7333333335 + 0.7333333335 + x = 1.933333333 + 0.7333333335 Combine like terms: -0.7333333335 + 0.7333333335 = 0.0000000000 0.0000000000 + x = 1.933333333 + 0.7333333335 x = 1.933333333 + 0.7333333335 Combine like terms: 1.933333333 + 0.7333333335 = 2.6666666665 x = 2.6666666665 Simplifying x = 2.6666666665

Subproblem 2

x + -0.7333333335 = -1.933333333 Simplifying x + -0.7333333335 = -1.933333333 Reorder the terms: -0.7333333335 + x = -1.933333333 Solving -0.7333333335 + x = -1.933333333 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7333333335' to each side of the equation. -0.7333333335 + 0.7333333335 + x = -1.933333333 + 0.7333333335 Combine like terms: -0.7333333335 + 0.7333333335 = 0.0000000000 0.0000000000 + x = -1.933333333 + 0.7333333335 x = -1.933333333 + 0.7333333335 Combine like terms: -1.933333333 + 0.7333333335 = -1.1999999995 x = -1.1999999995 Simplifying x = -1.1999999995

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.6666666665, -1.1999999995}

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