3x^2-8x-45=0

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Solution for 3x^2-8x-45=0 equation: 


Simplifying
3x2 + -8x + -45 = 0

Reorder the terms:
-45 + -8x + 3x2 = 0

Solving
-45 + -8x + 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'.
-15 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -2.666666667x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -2.666666667x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -2.666666667x + x2 = 0 + 15
-2.666666667x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-2.666666667x + x2 = 15

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 = 15 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 15 + 1.777777780

Combine like terms: 15 + 1.777777780 = 16.77777778
1.777777780 + -2.666666667x + x2 = 16.77777778

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 16.77777778

Calculate the square root of the right side: 4.096068576

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 4.096068576 and -4.096068576.


Subproblem 1
x + -1.333333334 = 4.096068576

Simplifying
x + -1.333333334 = 4.096068576

Reorder the terms:
-1.333333334 + x = 4.096068576

Solving
-1.333333334 + x = 4.096068576

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 = 4.096068576 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = 4.096068576 + 1.333333334
x = 4.096068576 + 1.333333334

Combine like terms: 4.096068576 + 1.333333334 = 5.42940191
x = 5.42940191

Simplifying
x = 5.42940191


Subproblem 2
x + -1.333333334 = -4.096068576

Simplifying
x + -1.333333334 = -4.096068576

Reorder the terms:
-1.333333334 + x = -4.096068576

Solving
-1.333333334 + x = -4.096068576

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 = -4.096068576 + 1.333333334

Combine like terms: -1.333333334 + 1.333333334 = 0.000000000
0.000000000 + x = -4.096068576 + 1.333333334
x = -4.096068576 + 1.333333334

Combine like terms: -4.096068576 + 1.333333334 = -2.762735242
x = -2.762735242

Simplifying
x = -2.762735242


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.42940191, -2.762735242}

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