3x^2+29x-7.5=0

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Solution for 3x^2+29x-7.5=0 equation: 


Simplifying
3x2 + 29x + -7.5 = 0

Reorder the terms:
-7.5 + 29x + 3x2 = 0

Solving
-7.5 + 29x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-2.5 + 9.666666667x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 9.666666667x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 9.666666667x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 9.666666667x + x2 = 0 + 2.5
9.666666667x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
9.666666667x + x2 = 2.5

The x term is 9.666666667x.  Take half its coefficient (4.833333334).
Square it (23.36111112) and add it to both sides.

Add '23.36111112' to each side of the equation.
9.666666667x + 23.36111112 + x2 = 2.5 + 23.36111112

Reorder the terms:
23.36111112 + 9.666666667x + x2 = 2.5 + 23.36111112

Combine like terms: 2.5 + 23.36111112 = 25.86111112
23.36111112 + 9.666666667x + x2 = 25.86111112

Factor a perfect square on the left side:
(x + 4.833333334)(x + 4.833333334) = 25.86111112

Calculate the square root of the right side: 5.085382102

Break this problem into two subproblems by setting 
(x + 4.833333334) equal to 5.085382102 and -5.085382102.


Subproblem 1
x + 4.833333334 = 5.085382102

Simplifying
x + 4.833333334 = 5.085382102

Reorder the terms:
4.833333334 + x = 5.085382102

Solving
4.833333334 + x = 5.085382102

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4.833333334' to each side of the equation.
4.833333334 + -4.833333334 + x = 5.085382102 + -4.833333334

Combine like terms: 4.833333334 + -4.833333334 = 0.000000000
0.000000000 + x = 5.085382102 + -4.833333334
x = 5.085382102 + -4.833333334

Combine like terms: 5.085382102 + -4.833333334 = 0.252048768
x = 0.252048768

Simplifying
x = 0.252048768


Subproblem 2
x + 4.833333334 = -5.085382102

Simplifying
x + 4.833333334 = -5.085382102

Reorder the terms:
4.833333334 + x = -5.085382102

Solving
4.833333334 + x = -5.085382102

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4.833333334' to each side of the equation.
4.833333334 + -4.833333334 + x = -5.085382102 + -4.833333334

Combine like terms: 4.833333334 + -4.833333334 = 0.000000000
0.000000000 + x = -5.085382102 + -4.833333334
x = -5.085382102 + -4.833333334

Combine like terms: -5.085382102 + -4.833333334 = -9.918715436
x = -9.918715436

Simplifying
x = -9.918715436


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.252048768, -9.918715436}

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