3x^2-14x-45=0

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Solution for 3x^2-14x-45=0 equation: 


Simplifying
3x2 + -14x + -45 = 0

Reorder the terms:
-45 + -14x + 3x2 = 0

Solving
-45 + -14x + 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 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -4.666666667x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -4.666666667x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -4.666666667x + x2 = 0 + 15
-4.666666667x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-4.666666667x + x2 = 15

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = 15 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 15 + 5.444444448

Combine like terms: 15 + 5.444444448 = 20.444444448
5.444444448 + -4.666666667x + x2 = 20.444444448

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 20.444444448

Calculate the square root of the right side: 4.521553322

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 4.521553322 and -4.521553322.


Subproblem 1
x + -2.333333334 = 4.521553322

Simplifying
x + -2.333333334 = 4.521553322

Reorder the terms:
-2.333333334 + x = 4.521553322

Solving
-2.333333334 + x = 4.521553322

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = 4.521553322 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 4.521553322 + 2.333333334
x = 4.521553322 + 2.333333334

Combine like terms: 4.521553322 + 2.333333334 = 6.854886656
x = 6.854886656

Simplifying
x = 6.854886656


Subproblem 2
x + -2.333333334 = -4.521553322

Simplifying
x + -2.333333334 = -4.521553322

Reorder the terms:
-2.333333334 + x = -4.521553322

Solving
-2.333333334 + x = -4.521553322

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = -4.521553322 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -4.521553322 + 2.333333334
x = -4.521553322 + 2.333333334

Combine like terms: -4.521553322 + 2.333333334 = -2.188219988
x = -2.188219988

Simplifying
x = -2.188219988


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.854886656, -2.188219988}

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