6x^2+28x-5=0

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Solution for 6x^2+28x-5=0 equation: 


Simplifying
6x2 + 28x + -5 = 0

Reorder the terms:
-5 + 28x + 6x2 = 0

Solving
-5 + 28x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-0.8333333333 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + 4.666666667x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + 4.666666667x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + 4.666666667x + x2 = 0 + 0.8333333333
4.666666667x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
4.666666667x + x2 = 0.8333333333

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = 0.8333333333 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = 0.8333333333 + 5.444444448

Combine like terms: 0.8333333333 + 5.444444448 = 6.2777777813
5.444444448 + 4.666666667x + x2 = 6.2777777813

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = 6.2777777813

Calculate the square root of the right side: 2.505549397

Break this problem into two subproblems by setting 
(x + 2.333333334) equal to 2.505549397 and -2.505549397.


Subproblem 1
x + 2.333333334 = 2.505549397

Simplifying
x + 2.333333334 = 2.505549397

Reorder the terms:
2.333333334 + x = 2.505549397

Solving
2.333333334 + x = 2.505549397

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = 2.505549397 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = 2.505549397 + -2.333333334
x = 2.505549397 + -2.333333334

Combine like terms: 2.505549397 + -2.333333334 = 0.172216063
x = 0.172216063

Simplifying
x = 0.172216063


Subproblem 2
x + 2.333333334 = -2.505549397

Simplifying
x + 2.333333334 = -2.505549397

Reorder the terms:
2.333333334 + x = -2.505549397

Solving
2.333333334 + x = -2.505549397

Solving for variable 'x'.

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

Add '-2.333333334' to each side of the equation.
2.333333334 + -2.333333334 + x = -2.505549397 + -2.333333334

Combine like terms: 2.333333334 + -2.333333334 = 0.000000000
0.000000000 + x = -2.505549397 + -2.333333334
x = -2.505549397 + -2.333333334

Combine like terms: -2.505549397 + -2.333333334 = -4.838882731
x = -4.838882731

Simplifying
x = -4.838882731


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.172216063, -4.838882731}

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