9x^2-24x+4=0

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Solution for 9x^2-24x+4=0 equation:


Simplifying
9x2 + -24x + 4 = 0

Reorder the terms:
4 + -24x + 9x2 = 0

Solving
4 + -24x + 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 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.4444444444' to each side of the equation.
0.4444444444 + -2.666666667x + -0.4444444444 + x2 = 0 + -0.4444444444

Reorder the terms:
0.4444444444 + -0.4444444444 + -2.666666667x + x2 = 0 + -0.4444444444

Combine like terms: 0.4444444444 + -0.4444444444 = 0.0000000000
0.0000000000 + -2.666666667x + x2 = 0 + -0.4444444444
-2.666666667x + x2 = 0 + -0.4444444444

Combine like terms: 0 + -0.4444444444 = -0.4444444444
-2.666666667x + x2 = -0.4444444444

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = -0.4444444444 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = -0.4444444444 + 1.777777780

Combine like terms: -0.4444444444 + 1.777777780 = 1.3333333356
1.777777780 + -2.666666667x + x2 = 1.3333333356

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 1.3333333356

Calculate the square root of the right side: 1.154700539

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 1.154700539 and -1.154700539.

Subproblem 1

x + -1.333333334 = 1.154700539 Simplifying x + -1.333333334 = 1.154700539 Reorder the terms: -1.333333334 + x = 1.154700539 Solving -1.333333334 + x = 1.154700539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 1.154700539 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.154700539 + 1.333333334 x = 1.154700539 + 1.333333334 Combine like terms: 1.154700539 + 1.333333334 = 2.488033873 x = 2.488033873 Simplifying x = 2.488033873

Subproblem 2

x + -1.333333334 = -1.154700539 Simplifying x + -1.333333334 = -1.154700539 Reorder the terms: -1.333333334 + x = -1.154700539 Solving -1.333333334 + x = -1.154700539 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -1.154700539 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.154700539 + 1.333333334 x = -1.154700539 + 1.333333334 Combine like terms: -1.154700539 + 1.333333334 = 0.178632795 x = 0.178632795 Simplifying x = 0.178632795

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.488033873, 0.178632795}

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