x^2=6x+11

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Solution for x^2=6x+11 equation:


Simplifying
x2 = 6x + 11

Reorder the terms:
x2 = 11 + 6x

Solving
x2 = 11 + 6x

Solving for variable 'x'.

Reorder the terms:
-11 + -6x + x2 = 11 + 6x + -11 + -6x

Reorder the terms:
-11 + -6x + x2 = 11 + -11 + 6x + -6x

Combine like terms: 11 + -11 = 0
-11 + -6x + x2 = 0 + 6x + -6x
-11 + -6x + x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-11 + -6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + -6x + 11 + x2 = 0 + 11

Reorder the terms:
-11 + 11 + -6x + x2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -6x + x2 = 0 + 11
-6x + x2 = 0 + 11

Combine like terms: 0 + 11 = 11
-6x + x2 = 11

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 11 + 9

Reorder the terms:
9 + -6x + x2 = 11 + 9

Combine like terms: 11 + 9 = 20
9 + -6x + x2 = 20

Factor a perfect square on the left side:
(x + -3)(x + -3) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(x + -3) equal to 4.472135955 and -4.472135955.

Subproblem 1

x + -3 = 4.472135955 Simplifying x + -3 = 4.472135955 Reorder the terms: -3 + x = 4.472135955 Solving -3 + x = 4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 4.472135955 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.472135955 + 3 x = 4.472135955 + 3 Combine like terms: 4.472135955 + 3 = 7.472135955 x = 7.472135955 Simplifying x = 7.472135955

Subproblem 2

x + -3 = -4.472135955 Simplifying x + -3 = -4.472135955 Reorder the terms: -3 + x = -4.472135955 Solving -3 + x = -4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -4.472135955 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.472135955 + 3 x = -4.472135955 + 3 Combine like terms: -4.472135955 + 3 = -1.472135955 x = -1.472135955 Simplifying x = -1.472135955

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.472135955, -1.472135955}

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