2u^2-9u+2=0

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Solution for 2u^2-9u+2=0 equation:


Simplifying
2u2 + -9u + 2 = 0

Reorder the terms:
2 + -9u + 2u2 = 0

Solving
2 + -9u + 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'.
1 + -4.5u + u2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -4.5u + -1 + u2 = 0 + -1

Reorder the terms:
1 + -1 + -4.5u + u2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4.5u + u2 = 0 + -1
-4.5u + u2 = 0 + -1

Combine like terms: 0 + -1 = -1
-4.5u + u2 = -1

The u term is -4.5u.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5u + 5.0625 + u2 = -1 + 5.0625

Reorder the terms:
5.0625 + -4.5u + u2 = -1 + 5.0625

Combine like terms: -1 + 5.0625 = 4.0625
5.0625 + -4.5u + u2 = 4.0625

Factor a perfect square on the left side:
(u + -2.25)(u + -2.25) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(u + -2.25) equal to 2.015564437 and -2.015564437.

Subproblem 1

u + -2.25 = 2.015564437 Simplifying u + -2.25 = 2.015564437 Reorder the terms: -2.25 + u = 2.015564437 Solving -2.25 + u = 2.015564437 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + u = 2.015564437 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + u = 2.015564437 + 2.25 u = 2.015564437 + 2.25 Combine like terms: 2.015564437 + 2.25 = 4.265564437 u = 4.265564437 Simplifying u = 4.265564437

Subproblem 2

u + -2.25 = -2.015564437 Simplifying u + -2.25 = -2.015564437 Reorder the terms: -2.25 + u = -2.015564437 Solving -2.25 + u = -2.015564437 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + u = -2.015564437 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + u = -2.015564437 + 2.25 u = -2.015564437 + 2.25 Combine like terms: -2.015564437 + 2.25 = 0.234435563 u = 0.234435563 Simplifying u = 0.234435563

Solution

The solution to the problem is based on the solutions from the subproblems. u = {4.265564437, 0.234435563}

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