-2.4X^2+7.3X+4.7=0

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Solution for -2.4X^2+7.3X+4.7=0 equation: 


Simplifying
-2.4X2 + 7.3X + 4.7 = 0

Reorder the terms:
4.7 + 7.3X + -2.4X2 = 0

Solving
4.7 + 7.3X + -2.4X2 = 0

Solving for variable 'X'.

Begin completing the square.  Divide all terms by
-2.4 the coefficient of the squared term: 

Divide each side by '-2.4'.
-1.958333333 + -3.041666667X + X2 = 0

Move the constant term to the right:

Add '1.958333333' to each side of the equation.
-1.958333333 + -3.041666667X + 1.958333333 + X2 = 0 + 1.958333333

Reorder the terms:
-1.958333333 + 1.958333333 + -3.041666667X + X2 = 0 + 1.958333333

Combine like terms: -1.958333333 + 1.958333333 = 0.000000000
0.000000000 + -3.041666667X + X2 = 0 + 1.958333333
-3.041666667X + X2 = 0 + 1.958333333

Combine like terms: 0 + 1.958333333 = 1.958333333
-3.041666667X + X2 = 1.958333333

The X term is -3.041666667X.  Take half its coefficient (-1.520833334).
Square it (2.312934030) and add it to both sides.

Add '2.312934030' to each side of the equation.
-3.041666667X + 2.312934030 + X2 = 1.958333333 + 2.312934030

Reorder the terms:
2.312934030 + -3.041666667X + X2 = 1.958333333 + 2.312934030

Combine like terms: 1.958333333 + 2.312934030 = 4.271267363
2.312934030 + -3.041666667X + X2 = 4.271267363

Factor a perfect square on the left side:
(X + -1.520833334)(X + -1.520833334) = 4.271267363

Calculate the square root of the right side: 2.066704469

Break this problem into two subproblems by setting 
(X + -1.520833334) equal to 2.066704469 and -2.066704469.


Subproblem 1
X + -1.520833334 = 2.066704469

Simplifying
X + -1.520833334 = 2.066704469

Reorder the terms:
-1.520833334 + X = 2.066704469

Solving
-1.520833334 + X = 2.066704469

Solving for variable 'X'.

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

Add '1.520833334' to each side of the equation.
-1.520833334 + 1.520833334 + X = 2.066704469 + 1.520833334

Combine like terms: -1.520833334 + 1.520833334 = 0.000000000
0.000000000 + X = 2.066704469 + 1.520833334
X = 2.066704469 + 1.520833334

Combine like terms: 2.066704469 + 1.520833334 = 3.587537803
X = 3.587537803

Simplifying
X = 3.587537803


Subproblem 2
X + -1.520833334 = -2.066704469

Simplifying
X + -1.520833334 = -2.066704469

Reorder the terms:
-1.520833334 + X = -2.066704469

Solving
-1.520833334 + X = -2.066704469

Solving for variable 'X'.

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

Add '1.520833334' to each side of the equation.
-1.520833334 + 1.520833334 + X = -2.066704469 + 1.520833334

Combine like terms: -1.520833334 + 1.520833334 = 0.000000000
0.000000000 + X = -2.066704469 + 1.520833334
X = -2.066704469 + 1.520833334

Combine like terms: -2.066704469 + 1.520833334 = -0.545871135
X = -0.545871135

Simplifying
X = -0.545871135


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {3.587537803, -0.545871135}

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