24x=-9x^2+5

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


Simplifying
24x = -9x2 + 5

Reorder the terms:
24x = 5 + -9x2

Solving
24x = 5 + -9x2

Solving for variable 'x'.

Reorder the terms:
-5 + 24x + 9x2 = 5 + -9x2 + -5 + 9x2

Reorder the terms:
-5 + 24x + 9x2 = 5 + -5 + -9x2 + 9x2

Combine like terms: 5 + -5 = 0
-5 + 24x + 9x2 = 0 + -9x2 + 9x2
-5 + 24x + 9x2 = -9x2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
-5 + 24x + 9x2 = 0

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 = 2.3333333356
1.777777780 + 2.666666667x + x2 = 2.3333333356

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 2.3333333356

Calculate the square root of the right side: 1.527525232

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 1.527525232 and -1.527525232.

Subproblem 1

x + 1.333333334 = 1.527525232 Simplifying x + 1.333333334 = 1.527525232 Reorder the terms: 1.333333334 + x = 1.527525232 Solving 1.333333334 + x = 1.527525232 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 = 1.527525232 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 1.527525232 + -1.333333334 x = 1.527525232 + -1.333333334 Combine like terms: 1.527525232 + -1.333333334 = 0.194191898 x = 0.194191898 Simplifying x = 0.194191898

Subproblem 2

x + 1.333333334 = -1.527525232 Simplifying x + 1.333333334 = -1.527525232 Reorder the terms: 1.333333334 + x = -1.527525232 Solving 1.333333334 + x = -1.527525232 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 = -1.527525232 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -1.527525232 + -1.333333334 x = -1.527525232 + -1.333333334 Combine like terms: -1.527525232 + -1.333333334 = -2.860858566 x = -2.860858566 Simplifying x = -2.860858566

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.194191898, -2.860858566}

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