x^2-7x-36=0

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Solution for x^2-7x-36=0 equation: 


Simplifying
x2 + -7x + -36 = 0

Reorder the terms:
-36 + -7x + x2 = 0

Solving
-36 + -7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + -7x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + -7x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + -7x + x2 = 0 + 36
-7x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
-7x + x2 = 36

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 36 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 36 + 12.25

Combine like terms: 36 + 12.25 = 48.25
12.25 + -7x + x2 = 48.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(x + -3.5) equal to 6.946221995 and -6.946221995.


Subproblem 1
x + -3.5 = 6.946221995

Simplifying
x + -3.5 = 6.946221995

Reorder the terms:
-3.5 + x = 6.946221995

Solving
-3.5 + x = 6.946221995

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 6.946221995 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 6.946221995 + 3.5
x = 6.946221995 + 3.5

Combine like terms: 6.946221995 + 3.5 = 10.446221995
x = 10.446221995

Simplifying
x = 10.446221995


Subproblem 2
x + -3.5 = -6.946221995

Simplifying
x + -3.5 = -6.946221995

Reorder the terms:
-3.5 + x = -6.946221995

Solving
-3.5 + x = -6.946221995

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -6.946221995 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -6.946221995 + 3.5
x = -6.946221995 + 3.5

Combine like terms: -6.946221995 + 3.5 = -3.446221995
x = -3.446221995

Simplifying
x = -3.446221995


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.446221995, -3.446221995}

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