x^2-11x+19=-2

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Solution for x^2-11x+19=-2 equation:


Simplifying
x2 + -11x + 19 = -2

Reorder the terms:
19 + -11x + x2 = -2

Solving
19 + -11x + x2 = -2

Solving for variable 'x'.

Reorder the terms:
19 + 2 + -11x + x2 = -2 + 2

Combine like terms: 19 + 2 = 21
21 + -11x + x2 = -2 + 2

Combine like terms: -2 + 2 = 0
21 + -11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + -11x + -21 + x2 = 0 + -21

Reorder the terms:
21 + -21 + -11x + x2 = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -11x + x2 = 0 + -21
-11x + x2 = 0 + -21

Combine like terms: 0 + -21 = -21
-11x + x2 = -21

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 = -21 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -21 + 30.25

Combine like terms: -21 + 30.25 = 9.25
30.25 + -11x + x2 = 9.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(x + -5.5) equal to 3.041381265 and -3.041381265.

Subproblem 1

x + -5.5 = 3.041381265 Simplifying x + -5.5 = 3.041381265 Reorder the terms: -5.5 + x = 3.041381265 Solving -5.5 + x = 3.041381265 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 = 3.041381265 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 3.041381265 + 5.5 x = 3.041381265 + 5.5 Combine like terms: 3.041381265 + 5.5 = 8.541381265 x = 8.541381265 Simplifying x = 8.541381265

Subproblem 2

x + -5.5 = -3.041381265 Simplifying x + -5.5 = -3.041381265 Reorder the terms: -5.5 + x = -3.041381265 Solving -5.5 + x = -3.041381265 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 = -3.041381265 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -3.041381265 + 5.5 x = -3.041381265 + 5.5 Combine like terms: -3.041381265 + 5.5 = 2.458618735 x = 2.458618735 Simplifying x = 2.458618735

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.541381265, 2.458618735}

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