u^2-4u+2=0

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Solution for u^2-4u+2=0 equation:


Simplifying
u2 + -4u + 2 = 0

Reorder the terms:
2 + -4u + u2 = 0

Solving
2 + -4u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -4u + -2 + u2 = 0 + -2

Reorder the terms:
2 + -2 + -4u + u2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -4u + u2 = 0 + -2
-4u + u2 = 0 + -2

Combine like terms: 0 + -2 = -2
-4u + u2 = -2

The u term is -4u.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4u + 4 + u2 = -2 + 4

Reorder the terms:
4 + -4u + u2 = -2 + 4

Combine like terms: -2 + 4 = 2
4 + -4u + u2 = 2

Factor a perfect square on the left side:
(u + -2)(u + -2) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(u + -2) equal to 1.414213562 and -1.414213562.

Subproblem 1

u + -2 = 1.414213562 Simplifying u + -2 = 1.414213562 Reorder the terms: -2 + u = 1.414213562 Solving -2 + u = 1.414213562 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + u = 1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + u = 1.414213562 + 2 u = 1.414213562 + 2 Combine like terms: 1.414213562 + 2 = 3.414213562 u = 3.414213562 Simplifying u = 3.414213562

Subproblem 2

u + -2 = -1.414213562 Simplifying u + -2 = -1.414213562 Reorder the terms: -2 + u = -1.414213562 Solving -2 + u = -1.414213562 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + u = -1.414213562 + 2 Combine like terms: -2 + 2 = 0 0 + u = -1.414213562 + 2 u = -1.414213562 + 2 Combine like terms: -1.414213562 + 2 = 0.585786438 u = 0.585786438 Simplifying u = 0.585786438

Solution

The solution to the problem is based on the solutions from the subproblems. u = {3.414213562, 0.585786438}

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