-x^2+11x-16=0

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Solution for -x^2+11x-16=0 equation:


Simplifying
-1x2 + 11x + -16 = 0

Reorder the terms:
-16 + 11x + -1x2 = 0

Solving
-16 + 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'.
16 + -11x + x2 = 0

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -11x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -11x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -11x + x2 = 0 + -16
-11x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-11x + x2 = -16

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 = -16 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -16 + 30.25

Combine like terms: -16 + 30.25 = 14.25
30.25 + -11x + x2 = 14.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + -5.5) equal to 3.774917218 and -3.774917218.

Subproblem 1

x + -5.5 = 3.774917218 Simplifying x + -5.5 = 3.774917218 Reorder the terms: -5.5 + x = 3.774917218 Solving -5.5 + x = 3.774917218 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 = 3.774917218 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 3.774917218 + 5.5 x = 3.774917218 + 5.5 Combine like terms: 3.774917218 + 5.5 = 9.274917218 x = 9.274917218 Simplifying x = 9.274917218

Subproblem 2

x + -5.5 = -3.774917218 Simplifying x + -5.5 = -3.774917218 Reorder the terms: -5.5 + x = -3.774917218 Solving -5.5 + x = -3.774917218 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 = -3.774917218 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -3.774917218 + 5.5 x = -3.774917218 + 5.5 Combine like terms: -3.774917218 + 5.5 = 1.725082782 x = 1.725082782 Simplifying x = 1.725082782

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.274917218, 1.725082782}

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