3x^2+8x=83

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Solution for 3x^2+8x=83 equation:


Simplifying
3x2 + 8x = 83

Reorder the terms:
8x + 3x2 = 83

Solving
8x + 3x2 = 83

Solving for variable 'x'.

Reorder the terms:
-83 + 8x + 3x2 = 83 + -83

Combine like terms: 83 + -83 = 0
-83 + 8x + 3x2 = 0

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

Divide each side by '3'.
-27.66666667 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '27.66666667' to each side of the equation.
-27.66666667 + 2.666666667x + 27.66666667 + x2 = 0 + 27.66666667

Reorder the terms:
-27.66666667 + 27.66666667 + 2.666666667x + x2 = 0 + 27.66666667

Combine like terms: -27.66666667 + 27.66666667 = 0.00000000
0.00000000 + 2.666666667x + x2 = 0 + 27.66666667
2.666666667x + x2 = 0 + 27.66666667

Combine like terms: 0 + 27.66666667 = 27.66666667
2.666666667x + x2 = 27.66666667

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = 27.66666667 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 27.66666667 + 1.777777780

Combine like terms: 27.66666667 + 1.777777780 = 29.44444445
1.777777780 + 2.666666667x + x2 = 29.44444445

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 29.44444445

Calculate the square root of the right side: 5.426273533

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 5.426273533 and -5.426273533.

Subproblem 1

x + 1.333333334 = 5.426273533 Simplifying x + 1.333333334 = 5.426273533 Reorder the terms: 1.333333334 + x = 5.426273533 Solving 1.333333334 + x = 5.426273533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 5.426273533 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 5.426273533 + -1.333333334 x = 5.426273533 + -1.333333334 Combine like terms: 5.426273533 + -1.333333334 = 4.092940199 x = 4.092940199 Simplifying x = 4.092940199

Subproblem 2

x + 1.333333334 = -5.426273533 Simplifying x + 1.333333334 = -5.426273533 Reorder the terms: 1.333333334 + x = -5.426273533 Solving 1.333333334 + x = -5.426273533 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -5.426273533 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -5.426273533 + -1.333333334 x = -5.426273533 + -1.333333334 Combine like terms: -5.426273533 + -1.333333334 = -6.759606867 x = -6.759606867 Simplifying x = -6.759606867

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.092940199, -6.759606867}

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