9x^2+24x-8=0

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Solution for 9x^2+24x-8=0 equation:


Simplifying
9x2 + 24x + -8 = 0

Reorder the terms:
-8 + 24x + 9x2 = 0

Solving
-8 + 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'.
-0.8888888889 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + 2.666666667x + 0.8888888889 + x2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + 2.666666667x + x2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + 2.666666667x + x2 = 0 + 0.8888888889
2.666666667x + x2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
2.666666667x + x2 = 0.8888888889

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 = 0.8888888889 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 0.8888888889 + 1.777777780

Combine like terms: 0.8888888889 + 1.777777780 = 2.6666666689
1.777777780 + 2.666666667x + x2 = 2.6666666689

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 2.6666666689

Calculate the square root of the right side: 1.632993163

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 1.632993163 and -1.632993163.

Subproblem 1

x + 1.333333334 = 1.632993163 Simplifying x + 1.333333334 = 1.632993163 Reorder the terms: 1.333333334 + x = 1.632993163 Solving 1.333333334 + x = 1.632993163 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 = 1.632993163 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 1.632993163 + -1.333333334 x = 1.632993163 + -1.333333334 Combine like terms: 1.632993163 + -1.333333334 = 0.299659829 x = 0.299659829 Simplifying x = 0.299659829

Subproblem 2

x + 1.333333334 = -1.632993163 Simplifying x + 1.333333334 = -1.632993163 Reorder the terms: 1.333333334 + x = -1.632993163 Solving 1.333333334 + x = -1.632993163 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 = -1.632993163 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -1.632993163 + -1.333333334 x = -1.632993163 + -1.333333334 Combine like terms: -1.632993163 + -1.333333334 = -2.966326497 x = -2.966326497 Simplifying x = -2.966326497

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.299659829, -2.966326497}

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