2u^2+17u-28=0

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Solution for 2u^2+17u-28=0 equation:


Simplifying
2u2 + 17u + -28 = 0

Reorder the terms:
-28 + 17u + 2u2 = 0

Solving
-28 + 17u + 2u2 = 0

Solving for variable 'u'.

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

Divide each side by '2'.
-14 + 8.5u + u2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + 8.5u + 14 + u2 = 0 + 14

Reorder the terms:
-14 + 14 + 8.5u + u2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 8.5u + u2 = 0 + 14
8.5u + u2 = 0 + 14

Combine like terms: 0 + 14 = 14
8.5u + u2 = 14

The u term is 8.5u.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5u + 18.0625 + u2 = 14 + 18.0625

Reorder the terms:
18.0625 + 8.5u + u2 = 14 + 18.0625

Combine like terms: 14 + 18.0625 = 32.0625
18.0625 + 8.5u + u2 = 32.0625

Factor a perfect square on the left side:
(u + 4.25)(u + 4.25) = 32.0625

Calculate the square root of the right side: 5.662375826

Break this problem into two subproblems by setting 
(u + 4.25) equal to 5.662375826 and -5.662375826.

Subproblem 1

u + 4.25 = 5.662375826 Simplifying u + 4.25 = 5.662375826 Reorder the terms: 4.25 + u = 5.662375826 Solving 4.25 + u = 5.662375826 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + u = 5.662375826 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + u = 5.662375826 + -4.25 u = 5.662375826 + -4.25 Combine like terms: 5.662375826 + -4.25 = 1.412375826 u = 1.412375826 Simplifying u = 1.412375826

Subproblem 2

u + 4.25 = -5.662375826 Simplifying u + 4.25 = -5.662375826 Reorder the terms: 4.25 + u = -5.662375826 Solving 4.25 + u = -5.662375826 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-4.25' to each side of the equation. 4.25 + -4.25 + u = -5.662375826 + -4.25 Combine like terms: 4.25 + -4.25 = 0.00 0.00 + u = -5.662375826 + -4.25 u = -5.662375826 + -4.25 Combine like terms: -5.662375826 + -4.25 = -9.912375826 u = -9.912375826 Simplifying u = -9.912375826

Solution

The solution to the problem is based on the solutions from the subproblems. u = {1.412375826, -9.912375826}

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