u^2+14u+15=0

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Solution for u^2+14u+15=0 equation:


Simplifying
u2 + 14u + 15 = 0

Reorder the terms:
15 + 14u + u2 = 0

Solving
15 + 14u + u2 = 0

Solving for variable 'u'.

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 14u + -15 + u2 = 0 + -15

Reorder the terms:
15 + -15 + 14u + u2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 14u + u2 = 0 + -15
14u + u2 = 0 + -15

Combine like terms: 0 + -15 = -15
14u + u2 = -15

The u term is 14u.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14u + 49 + u2 = -15 + 49

Reorder the terms:
49 + 14u + u2 = -15 + 49

Combine like terms: -15 + 49 = 34
49 + 14u + u2 = 34

Factor a perfect square on the left side:
(u + 7)(u + 7) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(u + 7) equal to 5.830951895 and -5.830951895.

Subproblem 1

u + 7 = 5.830951895 Simplifying u + 7 = 5.830951895 Reorder the terms: 7 + u = 5.830951895 Solving 7 + u = 5.830951895 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + u = 5.830951895 + -7 Combine like terms: 7 + -7 = 0 0 + u = 5.830951895 + -7 u = 5.830951895 + -7 Combine like terms: 5.830951895 + -7 = -1.169048105 u = -1.169048105 Simplifying u = -1.169048105

Subproblem 2

u + 7 = -5.830951895 Simplifying u + 7 = -5.830951895 Reorder the terms: 7 + u = -5.830951895 Solving 7 + u = -5.830951895 Solving for variable 'u'. Move all terms containing u to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + u = -5.830951895 + -7 Combine like terms: 7 + -7 = 0 0 + u = -5.830951895 + -7 u = -5.830951895 + -7 Combine like terms: -5.830951895 + -7 = -12.830951895 u = -12.830951895 Simplifying u = -12.830951895

Solution

The solution to the problem is based on the solutions from the subproblems. u = {-1.169048105, -12.830951895}

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