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 = 105.25
56.25 + 15x + x2 = 105.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 105.25

Calculate the square root of the right side: 10.259142264

Break this problem into two subproblems by setting 
(x + 7.5) equal to 10.259142264 and -10.259142264.


Subproblem 1
x + 7.5 = 10.259142264

Simplifying
x + 7.5 = 10.259142264

Reorder the terms:
7.5 + x = 10.259142264

Solving
7.5 + x = 10.259142264

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 = 10.259142264 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 10.259142264 + -7.5
x = 10.259142264 + -7.5

Combine like terms: 10.259142264 + -7.5 = 2.759142264
x = 2.759142264

Simplifying
x = 2.759142264


Subproblem 2
x + 7.5 = -10.259142264

Simplifying
x + 7.5 = -10.259142264

Reorder the terms:
7.5 + x = -10.259142264

Solving
7.5 + x = -10.259142264

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 = -10.259142264 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -10.259142264 + -7.5
x = -10.259142264 + -7.5

Combine like terms: -10.259142264 + -7.5 = -17.759142264
x = -17.759142264

Simplifying
x = -17.759142264


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.759142264, -17.759142264}

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