-(9x^2-24x+5)=0

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Solution for -(9x^2-24x+5)=0 equation:


Simplifying
-1(9x2 + -24x + 5) = 0

Reorder the terms:
-1(5 + -24x + 9x2) = 0
(5 * -1 + -24x * -1 + 9x2 * -1) = 0
(-5 + 24x + -9x2) = 0

Solving
-5 + 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'.
0.5555555556 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '-0.5555555556' to each side of the equation.
0.5555555556 + -2.666666667x + -0.5555555556 + x2 = 0 + -0.5555555556

Reorder the terms:
0.5555555556 + -0.5555555556 + -2.666666667x + x2 = 0 + -0.5555555556

Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000
0.0000000000 + -2.666666667x + x2 = 0 + -0.5555555556
-2.666666667x + x2 = 0 + -0.5555555556

Combine like terms: 0 + -0.5555555556 = -0.5555555556
-2.666666667x + x2 = -0.5555555556

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 = -0.5555555556 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = -0.5555555556 + 1.777777780

Combine like terms: -0.5555555556 + 1.777777780 = 1.2222222244
1.777777780 + -2.666666667x + x2 = 1.2222222244

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 1.2222222244

Calculate the square root of the right side: 1.105541598

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 1.105541598 and -1.105541598.

Subproblem 1

x + -1.333333334 = 1.105541598 Simplifying x + -1.333333334 = 1.105541598 Reorder the terms: -1.333333334 + x = 1.105541598 Solving -1.333333334 + x = 1.105541598 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 = 1.105541598 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 1.105541598 + 1.333333334 x = 1.105541598 + 1.333333334 Combine like terms: 1.105541598 + 1.333333334 = 2.438874932 x = 2.438874932 Simplifying x = 2.438874932

Subproblem 2

x + -1.333333334 = -1.105541598 Simplifying x + -1.333333334 = -1.105541598 Reorder the terms: -1.333333334 + x = -1.105541598 Solving -1.333333334 + x = -1.105541598 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 = -1.105541598 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -1.105541598 + 1.333333334 x = -1.105541598 + 1.333333334 Combine like terms: -1.105541598 + 1.333333334 = 0.227791736 x = 0.227791736 Simplifying x = 0.227791736

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.438874932, 0.227791736}

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