9x^2-54x+40=0

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Solution for 9x^2-54x+40=0 equation:


Simplifying
9x2 + -54x + 40 = 0

Reorder the terms:
40 + -54x + 9x2 = 0

Solving
40 + -54x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
4.444444444 + -6x + x2 = 0

Move the constant term to the right:

Add '-4.444444444' to each side of the equation.
4.444444444 + -6x + -4.444444444 + x2 = 0 + -4.444444444

Reorder the terms:
4.444444444 + -4.444444444 + -6x + x2 = 0 + -4.444444444

Combine like terms: 4.444444444 + -4.444444444 = 0.000000000
0.000000000 + -6x + x2 = 0 + -4.444444444
-6x + x2 = 0 + -4.444444444

Combine like terms: 0 + -4.444444444 = -4.444444444
-6x + x2 = -4.444444444

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 = -4.444444444 + 9

Reorder the terms:
9 + -6x + x2 = -4.444444444 + 9

Combine like terms: -4.444444444 + 9 = 4.555555556
9 + -6x + x2 = 4.555555556

Factor a perfect square on the left side:
(x + -3)(x + -3) = 4.555555556

Calculate the square root of the right side: 2.134374746

Break this problem into two subproblems by setting 
(x + -3) equal to 2.134374746 and -2.134374746.

Subproblem 1

x + -3 = 2.134374746 Simplifying x + -3 = 2.134374746 Reorder the terms: -3 + x = 2.134374746 Solving -3 + x = 2.134374746 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 = 2.134374746 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.134374746 + 3 x = 2.134374746 + 3 Combine like terms: 2.134374746 + 3 = 5.134374746 x = 5.134374746 Simplifying x = 5.134374746

Subproblem 2

x + -3 = -2.134374746 Simplifying x + -3 = -2.134374746 Reorder the terms: -3 + x = -2.134374746 Solving -3 + x = -2.134374746 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 = -2.134374746 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.134374746 + 3 x = -2.134374746 + 3 Combine like terms: -2.134374746 + 3 = 0.865625254 x = 0.865625254 Simplifying x = 0.865625254

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.134374746, 0.865625254}

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