3x^2+4x-45=0

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Solution for 3x^2+4x-45=0 equation: 


Simplifying
3x2 + 4x + -45 = 0

Reorder the terms:
-45 + 4x + 3x2 = 0

Solving
-45 + 4x + 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 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 1.333333333x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + 1.333333333x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + 1.333333333x + x2 = 0 + 15
1.333333333x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
1.333333333x + x2 = 15

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 15 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 15 + 0.4444444442

Combine like terms: 15 + 0.4444444442 = 15.4444444442
0.4444444442 + 1.333333333x + x2 = 15.4444444442

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 15.4444444442

Calculate the square root of the right side: 3.929942041

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 3.929942041 and -3.929942041.


Subproblem 1
x + 0.6666666665 = 3.929942041

Simplifying
x + 0.6666666665 = 3.929942041

Reorder the terms:
0.6666666665 + x = 3.929942041

Solving
0.6666666665 + x = 3.929942041

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = 3.929942041 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = 3.929942041 + -0.6666666665
x = 3.929942041 + -0.6666666665

Combine like terms: 3.929942041 + -0.6666666665 = 3.2632753745
x = 3.2632753745

Simplifying
x = 3.2632753745


Subproblem 2
x + 0.6666666665 = -3.929942041

Simplifying
x + 0.6666666665 = -3.929942041

Reorder the terms:
0.6666666665 + x = -3.929942041

Solving
0.6666666665 + x = -3.929942041

Solving for variable 'x'.

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

Add '-0.6666666665' to each side of the equation.
0.6666666665 + -0.6666666665 + x = -3.929942041 + -0.6666666665

Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000
0.0000000000 + x = -3.929942041 + -0.6666666665
x = -3.929942041 + -0.6666666665

Combine like terms: -3.929942041 + -0.6666666665 = -4.5966087075
x = -4.5966087075

Simplifying
x = -4.5966087075


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.2632753745, -4.5966087075}

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