x^2-15x-29=0

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Solution for x^2-15x-29=0 equation: 


Simplifying
x2 + -15x + -29 = 0

Reorder the terms:
-29 + -15x + x2 = 0

Solving
-29 + -15x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + -15x + 29 + x2 = 0 + 29

Reorder the terms:
-29 + 29 + -15x + x2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -15x + x2 = 0 + 29
-15x + x2 = 0 + 29

Combine like terms: 0 + 29 = 29
-15x + x2 = 29

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 = 29 + 56.25

Reorder the terms:
56.25 + -15x + x2 = 29 + 56.25

Combine like terms: 29 + 56.25 = 85.25
56.25 + -15x + x2 = 85.25

Factor a perfect square on the left side:
(x + -7.5)(x + -7.5) = 85.25

Calculate the square root of the right side: 9.233092656

Break this problem into two subproblems by setting 
(x + -7.5) equal to 9.233092656 and -9.233092656.


Subproblem 1
x + -7.5 = 9.233092656

Simplifying
x + -7.5 = 9.233092656

Reorder the terms:
-7.5 + x = 9.233092656

Solving
-7.5 + x = 9.233092656

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 = 9.233092656 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = 9.233092656 + 7.5
x = 9.233092656 + 7.5

Combine like terms: 9.233092656 + 7.5 = 16.733092656
x = 16.733092656

Simplifying
x = 16.733092656


Subproblem 2
x + -7.5 = -9.233092656

Simplifying
x + -7.5 = -9.233092656

Reorder the terms:
-7.5 + x = -9.233092656

Solving
-7.5 + x = -9.233092656

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 = -9.233092656 + 7.5

Combine like terms: -7.5 + 7.5 = 0.0
0.0 + x = -9.233092656 + 7.5
x = -9.233092656 + 7.5

Combine like terms: -9.233092656 + 7.5 = -1.733092656
x = -1.733092656

Simplifying
x = -1.733092656


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.733092656, -1.733092656}

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