x^2-18=11x

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Solution for x^2-18=11x equation:


Simplifying
x2 + -18 = 11x

Reorder the terms:
-18 + x2 = 11x

Solving
-18 + x2 = 11x

Solving for variable 'x'.

Reorder the terms:
-18 + -11x + x2 = 11x + -11x

Combine like terms: 11x + -11x = 0
-18 + -11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + -11x + 18 + x2 = 0 + 18

Reorder the terms:
-18 + 18 + -11x + x2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -11x + x2 = 0 + 18
-11x + x2 = 0 + 18

Combine like terms: 0 + 18 = 18
-11x + x2 = 18

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 = 18 + 30.25

Reorder the terms:
30.25 + -11x + x2 = 18 + 30.25

Combine like terms: 18 + 30.25 = 48.25
30.25 + -11x + x2 = 48.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 48.25

Calculate the square root of the right side: 6.946221995

Break this problem into two subproblems by setting 
(x + -5.5) equal to 6.946221995 and -6.946221995.

Subproblem 1

x + -5.5 = 6.946221995 Simplifying x + -5.5 = 6.946221995 Reorder the terms: -5.5 + x = 6.946221995 Solving -5.5 + x = 6.946221995 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 = 6.946221995 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 6.946221995 + 5.5 x = 6.946221995 + 5.5 Combine like terms: 6.946221995 + 5.5 = 12.446221995 x = 12.446221995 Simplifying x = 12.446221995

Subproblem 2

x + -5.5 = -6.946221995 Simplifying x + -5.5 = -6.946221995 Reorder the terms: -5.5 + x = -6.946221995 Solving -5.5 + x = -6.946221995 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 = -6.946221995 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -6.946221995 + 5.5 x = -6.946221995 + 5.5 Combine like terms: -6.946221995 + 5.5 = -1.446221995 x = -1.446221995 Simplifying x = -1.446221995

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.446221995, -1.446221995}

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