6u^2+10u-1=0

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Solution for 6u^2+10u-1=0 equation: 


Simplifying
6u2 + 10u + -1 = 0

Reorder the terms:
-1 + 10u + 6u2 = 0

Solving
-1 + 10u + 6u2 = 0

Solving for variable 'u'.

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

Divide each side by '6'.
-0.1666666667 + 1.666666667u + u2 = 0

Move the constant term to the right:

Add '0.1666666667' to each side of the equation.
-0.1666666667 + 1.666666667u + 0.1666666667 + u2 = 0 + 0.1666666667

Reorder the terms:
-0.1666666667 + 0.1666666667 + 1.666666667u + u2 = 0 + 0.1666666667

Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000
0.0000000000 + 1.666666667u + u2 = 0 + 0.1666666667
1.666666667u + u2 = 0 + 0.1666666667

Combine like terms: 0 + 0.1666666667 = 0.1666666667
1.666666667u + u2 = 0.1666666667

The u term is 1.666666667u.  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.
1.666666667u + 0.6944444447 + u2 = 0.1666666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667u + u2 = 0.1666666667 + 0.6944444447

Combine like terms: 0.1666666667 + 0.6944444447 = 0.8611111114
0.6944444447 + 1.666666667u + u2 = 0.8611111114

Factor a perfect square on the left side:
(u + 0.8333333335)(u + 0.8333333335) = 0.8611111114

Calculate the square root of the right side: 0.927960727

Break this problem into two subproblems by setting 
(u + 0.8333333335) equal to 0.927960727 and -0.927960727.


Subproblem 1
u + 0.8333333335 = 0.927960727

Simplifying
u + 0.8333333335 = 0.927960727

Reorder the terms:
0.8333333335 + u = 0.927960727

Solving
0.8333333335 + u = 0.927960727

Solving for variable 'u'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + u = 0.927960727 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + u = 0.927960727 + -0.8333333335
u = 0.927960727 + -0.8333333335

Combine like terms: 0.927960727 + -0.8333333335 = 0.0946273935
u = 0.0946273935

Simplifying
u = 0.0946273935


Subproblem 2
u + 0.8333333335 = -0.927960727

Simplifying
u + 0.8333333335 = -0.927960727

Reorder the terms:
0.8333333335 + u = -0.927960727

Solving
0.8333333335 + u = -0.927960727

Solving for variable 'u'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + u = -0.927960727 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + u = -0.927960727 + -0.8333333335
u = -0.927960727 + -0.8333333335

Combine like terms: -0.927960727 + -0.8333333335 = -1.7612940605
u = -1.7612940605

Simplifying
u = -1.7612940605


Solution
The solution to the problem is based on the solutions
from the subproblems.
u = {0.0946273935, -1.7612940605}

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