6x^2+10x-5=0

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Solution for 6x^2+10x-5=0 equation: 


Simplifying
6x2 + 10x + -5 = 0

Reorder the terms:
-5 + 10x + 6x2 = 0

Solving
-5 + 10x + 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 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + 1.666666667x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + 1.666666667x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + 1.666666667x + x2 = 0 + 0.8333333333
1.666666667x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
1.666666667x + x2 = 0.8333333333

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 0.8333333333 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 0.8333333333 + 0.6944444447

Combine like terms: 0.8333333333 + 0.6944444447 = 1.527777778
0.6944444447 + 1.666666667x + x2 = 1.527777778

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 1.527777778

Calculate the square root of the right side: 1.236033081

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 1.236033081 and -1.236033081.


Subproblem 1
x + 0.8333333335 = 1.236033081

Simplifying
x + 0.8333333335 = 1.236033081

Reorder the terms:
0.8333333335 + x = 1.236033081

Solving
0.8333333335 + x = 1.236033081

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 1.236033081 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 1.236033081 + -0.8333333335
x = 1.236033081 + -0.8333333335

Combine like terms: 1.236033081 + -0.8333333335 = 0.4026997475
x = 0.4026997475

Simplifying
x = 0.4026997475


Subproblem 2
x + 0.8333333335 = -1.236033081

Simplifying
x + 0.8333333335 = -1.236033081

Reorder the terms:
0.8333333335 + x = -1.236033081

Solving
0.8333333335 + x = -1.236033081

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -1.236033081 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -1.236033081 + -0.8333333335
x = -1.236033081 + -0.8333333335

Combine like terms: -1.236033081 + -0.8333333335 = -2.0693664145
x = -2.0693664145

Simplifying
x = -2.0693664145


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.4026997475, -2.0693664145}

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