-x^2+11x+7=0

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Solution for -x^2+11x+7=0 equation: 


Simplifying
-1x2 + 11x + 7 = 0

Reorder the terms:
7 + 11x + -1x2 = 0

Solving
7 + 11x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-7 + -11x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -11x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -11x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -11x + x2 = 0 + 7
-11x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-11x + x2 = 7

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 = 7 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 7 + 30.25

Combine like terms: 7 + 30.25 = 37.25
30.25 + -11x + x2 = 37.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 37.25

Calculate the square root of the right side: 6.103277808

Break this problem into two subproblems by setting 
(x + -5.5) equal to 6.103277808 and -6.103277808.


Subproblem 1
x + -5.5 = 6.103277808

Simplifying
x + -5.5 = 6.103277808

Reorder the terms:
-5.5 + x = 6.103277808

Solving
-5.5 + x = 6.103277808

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 = 6.103277808 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = 6.103277808 + 5.5
x = 6.103277808 + 5.5

Combine like terms: 6.103277808 + 5.5 = 11.603277808
x = 11.603277808

Simplifying
x = 11.603277808


Subproblem 2
x + -5.5 = -6.103277808

Simplifying
x + -5.5 = -6.103277808

Reorder the terms:
-5.5 + x = -6.103277808

Solving
-5.5 + x = -6.103277808

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 = -6.103277808 + 5.5

Combine like terms: -5.5 + 5.5 = 0.0
0.0 + x = -6.103277808 + 5.5
x = -6.103277808 + 5.5

Combine like terms: -6.103277808 + 5.5 = -0.603277808
x = -0.603277808

Simplifying
x = -0.603277808


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.603277808, -0.603277808}

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