18u^2+11u-14+15+4u^2=0

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Solution for 18u^2+11u-14+15+4u^2=0 equation:


Simplifying
18u2 + 11u + -14 + 15 + 4u2 = 0

Reorder the terms:
-14 + 15 + 11u + 18u2 + 4u2 = 0

Combine like terms: -14 + 15 = 1
1 + 11u + 18u2 + 4u2 = 0

Combine like terms: 18u2 + 4u2 = 22u2
1 + 11u + 22u2 = 0

Solving
1 + 11u + 22u2 = 0

Solving for variable 'u'.

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

Divide each side by '22'.
0.04545454545 + 0.5u + u2 = 0

Move the constant term to the right:

Add '-0.04545454545' to each side of the equation.
0.04545454545 + 0.5u + -0.04545454545 + u2 = 0 + -0.04545454545

Reorder the terms:
0.04545454545 + -0.04545454545 + 0.5u + u2 = 0 + -0.04545454545

Combine like terms: 0.04545454545 + -0.04545454545 = 0.00000000000
0.00000000000 + 0.5u + u2 = 0 + -0.04545454545
0.5u + u2 = 0 + -0.04545454545

Combine like terms: 0 + -0.04545454545 = -0.04545454545
0.5u + u2 = -0.04545454545

The u term is 0.5u.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5u + 0.0625 + u2 = -0.04545454545 + 0.0625

Reorder the terms:
0.0625 + 0.5u + u2 = -0.04545454545 + 0.0625

Combine like terms: -0.04545454545 + 0.0625 = 0.01704545455
0.0625 + 0.5u + u2 = 0.01704545455

Factor a perfect square on the left side:
(u + 0.25)(u + 0.25) = 0.01704545455

Calculate the square root of the right side: 0.130558242

Break this problem into two subproblems by setting 
(u + 0.25) equal to 0.130558242 and -0.130558242.

Subproblem 1

u + 0.25 = 0.130558242 Simplifying u + 0.25 = 0.130558242 Reorder the terms: 0.25 + u = 0.130558242 Solving 0.25 + u = 0.130558242 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + u = 0.130558242 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + u = 0.130558242 + -0.25 u = 0.130558242 + -0.25 Combine like terms: 0.130558242 + -0.25 = -0.119441758 u = -0.119441758 Simplifying u = -0.119441758

Subproblem 2

u + 0.25 = -0.130558242 Simplifying u + 0.25 = -0.130558242 Reorder the terms: 0.25 + u = -0.130558242 Solving 0.25 + u = -0.130558242 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + u = -0.130558242 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + u = -0.130558242 + -0.25 u = -0.130558242 + -0.25 Combine like terms: -0.130558242 + -0.25 = -0.380558242 u = -0.380558242 Simplifying u = -0.380558242

Solution

The solution to the problem is based on the solutions from the subproblems. u = {-0.119441758, -0.380558242}

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