u^2+2u=2

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Solution for u^2+2u=2 equation:


Simplifying
u2 + 2u = 2

Reorder the terms:
2u + u2 = 2

Solving
2u + u2 = 2

Solving for variable 'u'.

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

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

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The u term is 2u.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2u + 1 + u2 = 2 + 1

Reorder the terms:
1 + 2u + u2 = 2 + 1

Combine like terms: 2 + 1 = 3
1 + 2u + u2 = 3

Factor a perfect square on the left side:
(u + 1)(u + 1) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(u + 1) equal to 1.732050808 and -1.732050808.

Subproblem 1

u + 1 = 1.732050808 Simplifying u + 1 = 1.732050808 Reorder the terms: 1 + u = 1.732050808 Solving 1 + u = 1.732050808 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + u = 1.732050808 + -1 Combine like terms: 1 + -1 = 0 0 + u = 1.732050808 + -1 u = 1.732050808 + -1 Combine like terms: 1.732050808 + -1 = 0.732050808 u = 0.732050808 Simplifying u = 0.732050808

Subproblem 2

u + 1 = -1.732050808 Simplifying u + 1 = -1.732050808 Reorder the terms: 1 + u = -1.732050808 Solving 1 + u = -1.732050808 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + u = -1.732050808 + -1 Combine like terms: 1 + -1 = 0 0 + u = -1.732050808 + -1 u = -1.732050808 + -1 Combine like terms: -1.732050808 + -1 = -2.732050808 u = -2.732050808 Simplifying u = -2.732050808

Solution

The solution to the problem is based on the solutions from the subproblems. u = {0.732050808, -2.732050808}

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