x^2+15x+49=0

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Solution for x^2+15x+49=0 equation: 


Simplifying
x2 + 15x + 49 = 0

Reorder the terms:
49 + 15x + x2 = 0

Solving
49 + 15x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-49' to each side of the equation.
49 + 15x + -49 + x2 = 0 + -49

Reorder the terms:
49 + -49 + 15x + x2 = 0 + -49

Combine like terms: 49 + -49 = 0
0 + 15x + x2 = 0 + -49
15x + x2 = 0 + -49

Combine like terms: 0 + -49 = -49
15x + x2 = -49

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = -49 + 56.25

Reorder the terms:
56.25 + 15x + x2 = -49 + 56.25

Combine like terms: -49 + 56.25 = 7.25
56.25 + 15x + x2 = 7.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 7.25

Calculate the square root of the right side: 2.692582404

Break this problem into two subproblems by setting 
(x + 7.5) equal to 2.692582404 and -2.692582404.


Subproblem 1
x + 7.5 = 2.692582404

Simplifying
x + 7.5 = 2.692582404

Reorder the terms:
7.5 + x = 2.692582404

Solving
7.5 + x = 2.692582404

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 2.692582404 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 2.692582404 + -7.5
x = 2.692582404 + -7.5

Combine like terms: 2.692582404 + -7.5 = -4.807417596
x = -4.807417596

Simplifying
x = -4.807417596


Subproblem 2
x + 7.5 = -2.692582404

Simplifying
x + 7.5 = -2.692582404

Reorder the terms:
7.5 + x = -2.692582404

Solving
7.5 + x = -2.692582404

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -2.692582404 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -2.692582404 + -7.5
x = -2.692582404 + -7.5

Combine like terms: -2.692582404 + -7.5 = -10.192582404
x = -10.192582404

Simplifying
x = -10.192582404


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-4.807417596, -10.192582404}

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