-7.2x^2-33.1x+18.3=0

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Solution for -7.2x^2-33.1x+18.3=0 equation:


Simplifying
-7.2x2 + -33.1x + 18.3 = 0

Reorder the terms:
18.3 + -33.1x + -7.2x2 = 0

Solving
18.3 + -33.1x + -7.2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-7.2 the coefficient of the squared term: 

Divide each side by '-7.2'.
-2.541666667 + 4.597222222x + x2 = 0

Move the constant term to the right:

Add '2.541666667' to each side of the equation.
-2.541666667 + 4.597222222x + 2.541666667 + x2 = 0 + 2.541666667

Reorder the terms:
-2.541666667 + 2.541666667 + 4.597222222x + x2 = 0 + 2.541666667

Combine like terms: -2.541666667 + 2.541666667 = 0.000000000
0.000000000 + 4.597222222x + x2 = 0 + 2.541666667
4.597222222x + x2 = 0 + 2.541666667

Combine like terms: 0 + 2.541666667 = 2.541666667
4.597222222x + x2 = 2.541666667

The x term is 4.597222222x.  Take half its coefficient (2.298611111).
Square it (5.283613040) and add it to both sides.

Add '5.283613040' to each side of the equation.
4.597222222x + 5.283613040 + x2 = 2.541666667 + 5.283613040

Reorder the terms:
5.283613040 + 4.597222222x + x2 = 2.541666667 + 5.283613040

Combine like terms: 2.541666667 + 5.283613040 = 7.825279707
5.283613040 + 4.597222222x + x2 = 7.825279707

Factor a perfect square on the left side:
(x + 2.298611111)(x + 2.298611111) = 7.825279707

Calculate the square root of the right side: 2.797370141

Break this problem into two subproblems by setting 
(x + 2.298611111) equal to 2.797370141 and -2.797370141.

Subproblem 1

x + 2.298611111 = 2.797370141 Simplifying x + 2.298611111 = 2.797370141 Reorder the terms: 2.298611111 + x = 2.797370141 Solving 2.298611111 + x = 2.797370141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.298611111' to each side of the equation. 2.298611111 + -2.298611111 + x = 2.797370141 + -2.298611111 Combine like terms: 2.298611111 + -2.298611111 = 0.000000000 0.000000000 + x = 2.797370141 + -2.298611111 x = 2.797370141 + -2.298611111 Combine like terms: 2.797370141 + -2.298611111 = 0.49875903 x = 0.49875903 Simplifying x = 0.49875903

Subproblem 2

x + 2.298611111 = -2.797370141 Simplifying x + 2.298611111 = -2.797370141 Reorder the terms: 2.298611111 + x = -2.797370141 Solving 2.298611111 + x = -2.797370141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.298611111' to each side of the equation. 2.298611111 + -2.298611111 + x = -2.797370141 + -2.298611111 Combine like terms: 2.298611111 + -2.298611111 = 0.000000000 0.000000000 + x = -2.797370141 + -2.298611111 x = -2.797370141 + -2.298611111 Combine like terms: -2.797370141 + -2.298611111 = -5.095981252 x = -5.095981252 Simplifying x = -5.095981252

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.49875903, -5.095981252}

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