9x^2-18x+4=0

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Solution for 9x^2-18x+4=0 equation:


Simplifying
9x2 + -18x + 4 = 0

Reorder the terms:
4 + -18x + 9x2 = 0

Solving
4 + -18x + 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'.
0.4444444444 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.4444444444' to each side of the equation.
0.4444444444 + -2x + -0.4444444444 + x2 = 0 + -0.4444444444

Reorder the terms:
0.4444444444 + -0.4444444444 + -2x + x2 = 0 + -0.4444444444

Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000
0.0000000000 + -2x + x2 = 0 + -0.4444444444
-2x + x2 = 0 + -0.4444444444

Combine like terms: 0 + -0.4444444444 = -0.4444444444
-2x + x2 = -0.4444444444

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -0.4444444444 + 1

Reorder the terms:
1 + -2x + x2 = -0.4444444444 + 1

Combine like terms: -0.4444444444 + 1 = 0.5555555556
1 + -2x + x2 = 0.5555555556

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.5555555556

Calculate the square root of the right side: 0.745355993

Break this problem into two subproblems by setting 
(x + -1) equal to 0.745355993 and -0.745355993.

Subproblem 1

x + -1 = 0.745355993 Simplifying x + -1 = 0.745355993 Reorder the terms: -1 + x = 0.745355993 Solving -1 + x = 0.745355993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 0.745355993 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.745355993 + 1 x = 0.745355993 + 1 Combine like terms: 0.745355993 + 1 = 1.745355993 x = 1.745355993 Simplifying x = 1.745355993

Subproblem 2

x + -1 = -0.745355993 Simplifying x + -1 = -0.745355993 Reorder the terms: -1 + x = -0.745355993 Solving -1 + x = -0.745355993 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -0.745355993 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.745355993 + 1 x = -0.745355993 + 1 Combine like terms: -0.745355993 + 1 = 0.254644007 x = 0.254644007 Simplifying x = 0.254644007

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.745355993, 0.254644007}

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