3x^2+25x-84=0

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Solution for 3x^2+25x-84=0 equation: 


Simplifying
3x2 + 25x + -84 = 0

Reorder the terms:
-84 + 25x + 3x2 = 0

Solving
-84 + 25x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-28 + 8.333333333x + x2 = 0

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + 8.333333333x + 28 + x2 = 0 + 28

Reorder the terms:
-28 + 28 + 8.333333333x + x2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + 8.333333333x + x2 = 0 + 28
8.333333333x + x2 = 0 + 28

Combine like terms: 0 + 28 = 28
8.333333333x + x2 = 28

The x term is 8.333333333x.  Take half its coefficient (4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
8.333333333x + 17.36111111 + x2 = 28 + 17.36111111

Reorder the terms:
17.36111111 + 8.333333333x + x2 = 28 + 17.36111111

Combine like terms: 28 + 17.36111111 = 45.36111111
17.36111111 + 8.333333333x + x2 = 45.36111111

Factor a perfect square on the left side:
(x + 4.166666667)(x + 4.166666667) = 45.36111111

Calculate the square root of the right side: 6.735065784

Break this problem into two subproblems by setting 
(x + 4.166666667) equal to 6.735065784 and -6.735065784.


Subproblem 1
x + 4.166666667 = 6.735065784

Simplifying
x + 4.166666667 = 6.735065784

Reorder the terms:
4.166666667 + x = 6.735065784

Solving
4.166666667 + x = 6.735065784

Solving for variable 'x'.

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

Add '-4.166666667' to each side of the equation.
4.166666667 + -4.166666667 + x = 6.735065784 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + x = 6.735065784 + -4.166666667
x = 6.735065784 + -4.166666667

Combine like terms: 6.735065784 + -4.166666667 = 2.568399117
x = 2.568399117

Simplifying
x = 2.568399117


Subproblem 2
x + 4.166666667 = -6.735065784

Simplifying
x + 4.166666667 = -6.735065784

Reorder the terms:
4.166666667 + x = -6.735065784

Solving
4.166666667 + x = -6.735065784

Solving for variable 'x'.

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

Add '-4.166666667' to each side of the equation.
4.166666667 + -4.166666667 + x = -6.735065784 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + x = -6.735065784 + -4.166666667
x = -6.735065784 + -4.166666667

Combine like terms: -6.735065784 + -4.166666667 = -10.901732451
x = -10.901732451

Simplifying
x = -10.901732451


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.568399117, -10.901732451}

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