4.5x^2-9x+4=0

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Solution for 4.5x^2-9x+4=0 equation:


Simplifying
4.5x2 + -9x + 4 = 0

Reorder the terms:
4 + -9x + 4.5x2 = 0

Solving
4 + -9x + 4.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '4.5'.
0.8888888889 + -2x + x2 = 0

Move the constant term to the right:

Add '-0.8888888889' to each side of the equation.
0.8888888889 + -2x + -0.8888888889 + x2 = 0 + -0.8888888889

Reorder the terms:
0.8888888889 + -0.8888888889 + -2x + x2 = 0 + -0.8888888889

Combine like terms: 0.8888888889 + -0.8888888889 = 0.0000000000
0.0000000000 + -2x + x2 = 0 + -0.8888888889
-2x + x2 = 0 + -0.8888888889

Combine like terms: 0 + -0.8888888889 = -0.8888888889
-2x + x2 = -0.8888888889

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 = -0.8888888889 + 1

Reorder the terms:
1 + -2x + x2 = -0.8888888889 + 1

Combine like terms: -0.8888888889 + 1 = 0.1111111111
1 + -2x + x2 = 0.1111111111

Factor a perfect square on the left side:
(x + -1)(x + -1) = 0.1111111111

Calculate the square root of the right side: 0.333333333

Break this problem into two subproblems by setting 
(x + -1) equal to 0.333333333 and -0.333333333.

Subproblem 1

x + -1 = 0.333333333 Simplifying x + -1 = 0.333333333 Reorder the terms: -1 + x = 0.333333333 Solving -1 + x = 0.333333333 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 = 0.333333333 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0.333333333 + 1 x = 0.333333333 + 1 Combine like terms: 0.333333333 + 1 = 1.333333333 x = 1.333333333 Simplifying x = 1.333333333

Subproblem 2

x + -1 = -0.333333333 Simplifying x + -1 = -0.333333333 Reorder the terms: -1 + x = -0.333333333 Solving -1 + x = -0.333333333 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 = -0.333333333 + 1 Combine like terms: -1 + 1 = 0 0 + x = -0.333333333 + 1 x = -0.333333333 + 1 Combine like terms: -0.333333333 + 1 = 0.666666667 x = 0.666666667 Simplifying x = 0.666666667

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.333333333, 0.666666667}

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