84=3x^2+8x

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Solution for 84=3x^2+8x equation:


Simplifying
84 = 3x2 + 8x

Reorder the terms:
84 = 8x + 3x2

Solving
84 = 8x + 3x2

Solving for variable 'x'.

Reorder the terms:
84 + -8x + -3x2 = 8x + -8x + 3x2 + -3x2

Combine like terms: 8x + -8x = 0
84 + -8x + -3x2 = 0 + 3x2 + -3x2
84 + -8x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
84 + -8x + -3x2 = 0

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

Divide each side by '-3'.
-28 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 2.666666667x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + 2.666666667x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 2.666666667x + x2 = 0 + 28
2.666666667x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
2.666666667x + x2 = 28

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 = 28 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 28 + 1.777777780

Combine like terms: 28 + 1.777777780 = 29.77777778
1.777777780 + 2.666666667x + x2 = 29.77777778

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 29.77777778

Calculate the square root of the right side: 5.456901848

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 5.456901848 and -5.456901848.

Subproblem 1

x + 1.333333334 = 5.456901848 Simplifying x + 1.333333334 = 5.456901848 Reorder the terms: 1.333333334 + x = 5.456901848 Solving 1.333333334 + x = 5.456901848 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 = 5.456901848 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 5.456901848 + -1.333333334 x = 5.456901848 + -1.333333334 Combine like terms: 5.456901848 + -1.333333334 = 4.123568514 x = 4.123568514 Simplifying x = 4.123568514

Subproblem 2

x + 1.333333334 = -5.456901848 Simplifying x + 1.333333334 = -5.456901848 Reorder the terms: 1.333333334 + x = -5.456901848 Solving 1.333333334 + x = -5.456901848 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 = -5.456901848 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -5.456901848 + -1.333333334 x = -5.456901848 + -1.333333334 Combine like terms: -5.456901848 + -1.333333334 = -6.790235182 x = -6.790235182 Simplifying x = -6.790235182

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.123568514, -6.790235182}

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