3x^2+29x-4.5=0

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Solution for 3x^2+29x-4.5=0 equation: 


Simplifying
3x2 + 29x + -4.5 = 0

Reorder the terms:
-4.5 + 29x + 3x2 = 0

Solving
-4.5 + 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'.
-1.5 + 9.666666667x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 9.666666667x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 9.666666667x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 9.666666667x + x2 = 0 + 1.5
9.666666667x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
9.666666667x + x2 = 1.5

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 = 1.5 + 23.36111112

Reorder the terms:
23.36111112 + 9.666666667x + x2 = 1.5 + 23.36111112

Combine like terms: 1.5 + 23.36111112 = 24.86111112
23.36111112 + 9.666666667x + x2 = 24.86111112

Factor a perfect square on the left side:
(x + 4.833333334)(x + 4.833333334) = 24.86111112

Calculate the square root of the right side: 4.986091768

Break this problem into two subproblems by setting 
(x + 4.833333334) equal to 4.986091768 and -4.986091768.


Subproblem 1
x + 4.833333334 = 4.986091768

Simplifying
x + 4.833333334 = 4.986091768

Reorder the terms:
4.833333334 + x = 4.986091768

Solving
4.833333334 + x = 4.986091768

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 = 4.986091768 + -4.833333334

Combine like terms: 4.833333334 + -4.833333334 = 0.000000000
0.000000000 + x = 4.986091768 + -4.833333334
x = 4.986091768 + -4.833333334

Combine like terms: 4.986091768 + -4.833333334 = 0.152758434
x = 0.152758434

Simplifying
x = 0.152758434


Subproblem 2
x + 4.833333334 = -4.986091768

Simplifying
x + 4.833333334 = -4.986091768

Reorder the terms:
4.833333334 + x = -4.986091768

Solving
4.833333334 + x = -4.986091768

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 = -4.986091768 + -4.833333334

Combine like terms: 4.833333334 + -4.833333334 = 0.000000000
0.000000000 + x = -4.986091768 + -4.833333334
x = -4.986091768 + -4.833333334

Combine like terms: -4.986091768 + -4.833333334 = -9.819425102
x = -9.819425102

Simplifying
x = -9.819425102


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.152758434, -9.819425102}

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