5x=x^2-6x+9

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Solution for 5x=x^2-6x+9 equation:


Simplifying
5x = x2 + -6x + 9

Reorder the terms:
5x = 9 + -6x + x2

Solving
5x = 9 + -6x + x2

Solving for variable 'x'.

Reorder the terms:
-9 + 5x + 6x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2

Combine like terms: 5x + 6x = 11x
-9 + 11x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2

Reorder the terms:
-9 + 11x + -1x2 = 9 + -9 + -6x + 6x + x2 + -1x2

Combine like terms: 9 + -9 = 0
-9 + 11x + -1x2 = 0 + -6x + 6x + x2 + -1x2
-9 + 11x + -1x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
-9 + 11x + -1x2 = 0 + x2 + -1x2
-9 + 11x + -1x2 = x2 + -1x2

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

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

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

Move the constant term to the right:

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

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

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

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

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 = -9 + 30.25

Reorder the terms:
30.25 + -11x + x2 = -9 + 30.25

Combine like terms: -9 + 30.25 = 21.25
30.25 + -11x + x2 = 21.25

Factor a perfect square on the left side:
(x + -5.5)(x + -5.5) = 21.25

Calculate the square root of the right side: 4.609772229

Break this problem into two subproblems by setting 
(x + -5.5) equal to 4.609772229 and -4.609772229.

Subproblem 1

x + -5.5 = 4.609772229 Simplifying x + -5.5 = 4.609772229 Reorder the terms: -5.5 + x = 4.609772229 Solving -5.5 + x = 4.609772229 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 = 4.609772229 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 4.609772229 + 5.5 x = 4.609772229 + 5.5 Combine like terms: 4.609772229 + 5.5 = 10.109772229 x = 10.109772229 Simplifying x = 10.109772229

Subproblem 2

x + -5.5 = -4.609772229 Simplifying x + -5.5 = -4.609772229 Reorder the terms: -5.5 + x = -4.609772229 Solving -5.5 + x = -4.609772229 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 = -4.609772229 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -4.609772229 + 5.5 x = -4.609772229 + 5.5 Combine like terms: -4.609772229 + 5.5 = 0.890227771 x = 0.890227771 Simplifying x = 0.890227771

Solution

The solution to the problem is based on the solutions from the subproblems. x = {10.109772229, 0.890227771}

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