u^2-10u-9=0

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Solution for u^2-10u-9=0 equation:


Simplifying
u2 + -10u + -9 = 0

Reorder the terms:
-9 + -10u + u2 = 0

Solving
-9 + -10u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -10u + 9 + u2 = 0 + 9

Reorder the terms:
-9 + 9 + -10u + u2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -10u + u2 = 0 + 9
-10u + u2 = 0 + 9

Combine like terms: 0 + 9 = 9
-10u + u2 = 9

The u term is -10u.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10u + 25 + u2 = 9 + 25

Reorder the terms:
25 + -10u + u2 = 9 + 25

Combine like terms: 9 + 25 = 34
25 + -10u + u2 = 34

Factor a perfect square on the left side:
(u + -5)(u + -5) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(u + -5) equal to 5.830951895 and -5.830951895.

Subproblem 1

u + -5 = 5.830951895 Simplifying u + -5 = 5.830951895 Reorder the terms: -5 + u = 5.830951895 Solving -5 + u = 5.830951895 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + u = 5.830951895 + 5 Combine like terms: -5 + 5 = 0 0 + u = 5.830951895 + 5 u = 5.830951895 + 5 Combine like terms: 5.830951895 + 5 = 10.830951895 u = 10.830951895 Simplifying u = 10.830951895

Subproblem 2

u + -5 = -5.830951895 Simplifying u + -5 = -5.830951895 Reorder the terms: -5 + u = -5.830951895 Solving -5 + u = -5.830951895 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + u = -5.830951895 + 5 Combine like terms: -5 + 5 = 0 0 + u = -5.830951895 + 5 u = -5.830951895 + 5 Combine like terms: -5.830951895 + 5 = -0.830951895 u = -0.830951895 Simplifying u = -0.830951895

Solution

The solution to the problem is based on the solutions from the subproblems. u = {10.830951895, -0.830951895}

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