x^2+11x-74=0

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Solution for x^2+11x-74=0 equation: 


Simplifying
x2 + 11x + -74 = 0

Reorder the terms:
-74 + 11x + x2 = 0

Solving
-74 + 11x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '74' to each side of the equation.
-74 + 11x + 74 + x2 = 0 + 74

Reorder the terms:
-74 + 74 + 11x + x2 = 0 + 74

Combine like terms: -74 + 74 = 0
0 + 11x + x2 = 0 + 74
11x + x2 = 0 + 74

Combine like terms: 0 + 74 = 74
11x + x2 = 74

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = 74 + 30.25

Reorder the terms:
30.25 + 11x + x2 = 74 + 30.25

Combine like terms: 74 + 30.25 = 104.25
30.25 + 11x + x2 = 104.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 104.25

Calculate the square root of the right side: 10.210288928

Break this problem into two subproblems by setting 
(x + 5.5) equal to 10.210288928 and -10.210288928.


Subproblem 1
x + 5.5 = 10.210288928

Simplifying
x + 5.5 = 10.210288928

Reorder the terms:
5.5 + x = 10.210288928

Solving
5.5 + x = 10.210288928

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 10.210288928 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 10.210288928 + -5.5
x = 10.210288928 + -5.5

Combine like terms: 10.210288928 + -5.5 = 4.710288928
x = 4.710288928

Simplifying
x = 4.710288928


Subproblem 2
x + 5.5 = -10.210288928

Simplifying
x + 5.5 = -10.210288928

Reorder the terms:
5.5 + x = -10.210288928

Solving
5.5 + x = -10.210288928

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -10.210288928 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -10.210288928 + -5.5
x = -10.210288928 + -5.5

Combine like terms: -10.210288928 + -5.5 = -15.710288928
x = -15.710288928

Simplifying
x = -15.710288928


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.710288928, -15.710288928}

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