x^2-2x+1=9x+12

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Solution for x^2-2x+1=9x+12 equation:


Simplifying
x2 + -2x + 1 = 9x + 12

Reorder the terms:
1 + -2x + x2 = 9x + 12

Reorder the terms:
1 + -2x + x2 = 12 + 9x

Solving
1 + -2x + x2 = 12 + 9x

Solving for variable 'x'.

Reorder the terms:
1 + -12 + -2x + -9x + x2 = 12 + 9x + -12 + -9x

Combine like terms: 1 + -12 = -11
-11 + -2x + -9x + x2 = 12 + 9x + -12 + -9x

Combine like terms: -2x + -9x = -11x
-11 + -11x + x2 = 12 + 9x + -12 + -9x

Reorder the terms:
-11 + -11x + x2 = 12 + -12 + 9x + -9x

Combine like terms: 12 + -12 = 0
-11 + -11x + x2 = 0 + 9x + -9x
-11 + -11x + x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-11 + -11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 11 + 30.25

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

Combine like terms: 11 + 30.25 = 41.25
30.25 + -11x + x2 = 41.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 41.25

Calculate the square root of the right side: 6.422616289

Break this problem into two subproblems by setting 
(x + -5.5) equal to 6.422616289 and -6.422616289.

Subproblem 1

x + -5.5 = 6.422616289 Simplifying x + -5.5 = 6.422616289 Reorder the terms: -5.5 + x = 6.422616289 Solving -5.5 + x = 6.422616289 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 = 6.422616289 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 6.422616289 + 5.5 x = 6.422616289 + 5.5 Combine like terms: 6.422616289 + 5.5 = 11.922616289 x = 11.922616289 Simplifying x = 11.922616289

Subproblem 2

x + -5.5 = -6.422616289 Simplifying x + -5.5 = -6.422616289 Reorder the terms: -5.5 + x = -6.422616289 Solving -5.5 + x = -6.422616289 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 = -6.422616289 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -6.422616289 + 5.5 x = -6.422616289 + 5.5 Combine like terms: -6.422616289 + 5.5 = -0.922616289 x = -0.922616289 Simplifying x = -0.922616289

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.922616289, -0.922616289}

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