12=x(x)-9x+23

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Solution for 12=x(x)-9x+23 equation:


Simplifying
12 = x(x) + -9x + 23

Multiply x * x
12 = x2 + -9x + 23

Reorder the terms:
12 = 23 + -9x + x2

Solving
12 = 23 + -9x + x2

Solving for variable 'x'.

Combine like terms: 12 + -23 = -11
-11 + 9x + -1x2 = 23 + -9x + x2 + -23 + 9x + -1x2

Reorder the terms:
-11 + 9x + -1x2 = 23 + -23 + -9x + 9x + x2 + -1x2

Combine like terms: 23 + -23 = 0
-11 + 9x + -1x2 = 0 + -9x + 9x + x2 + -1x2
-11 + 9x + -1x2 = -9x + 9x + x2 + -1x2

Combine like terms: -9x + 9x = 0
-11 + 9x + -1x2 = 0 + x2 + -1x2
-11 + 9x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-11 + 9x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
11 + -9x + x2 = 0

Move the constant term to the right:

Add '-11' to each side of the equation.
11 + -9x + -11 + x2 = 0 + -11

Reorder the terms:
11 + -11 + -9x + x2 = 0 + -11

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

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

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -11 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -11 + 20.25

Combine like terms: -11 + 20.25 = 9.25
20.25 + -9x + x2 = 9.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(x + -4.5) equal to 3.041381265 and -3.041381265.

Subproblem 1

x + -4.5 = 3.041381265 Simplifying x + -4.5 = 3.041381265 Reorder the terms: -4.5 + x = 3.041381265 Solving -4.5 + x = 3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 3.041381265 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 3.041381265 + 4.5 x = 3.041381265 + 4.5 Combine like terms: 3.041381265 + 4.5 = 7.541381265 x = 7.541381265 Simplifying x = 7.541381265

Subproblem 2

x + -4.5 = -3.041381265 Simplifying x + -4.5 = -3.041381265 Reorder the terms: -4.5 + x = -3.041381265 Solving -4.5 + x = -3.041381265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -3.041381265 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -3.041381265 + 4.5 x = -3.041381265 + 4.5 Combine like terms: -3.041381265 + 4.5 = 1.458618735 x = 1.458618735 Simplifying x = 1.458618735

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.541381265, 1.458618735}

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