3x^2+15x-138=0

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Solution for 3x^2+15x-138=0 equation: 


Simplifying
3x2 + 15x + -138 = 0

Reorder the terms:
-138 + 15x + 3x2 = 0

Solving
-138 + 15x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-46 + 5x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-46 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
-46 + 5x + x2 = 0

Solving
-46 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '46' to each side of the equation.
-46 + 5x + 46 + x2 = 0 + 46

Reorder the terms:
-46 + 46 + 5x + x2 = 0 + 46

Combine like terms: -46 + 46 = 0
0 + 5x + x2 = 0 + 46
5x + x2 = 0 + 46

Combine like terms: 0 + 46 = 46
5x + x2 = 46

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 46 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 46 + 6.25

Combine like terms: 46 + 6.25 = 52.25
6.25 + 5x + x2 = 52.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 52.25

Calculate the square root of the right side: 7.228416147

Break this problem into two subproblems by setting 
(x + 2.5) equal to 7.228416147 and -7.228416147.


Subproblem 1
x + 2.5 = 7.228416147

Simplifying
x + 2.5 = 7.228416147

Reorder the terms:
2.5 + x = 7.228416147

Solving
2.5 + x = 7.228416147

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 7.228416147 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 7.228416147 + -2.5
x = 7.228416147 + -2.5

Combine like terms: 7.228416147 + -2.5 = 4.728416147
x = 4.728416147

Simplifying
x = 4.728416147


Subproblem 2
x + 2.5 = -7.228416147

Simplifying
x + 2.5 = -7.228416147

Reorder the terms:
2.5 + x = -7.228416147

Solving
2.5 + x = -7.228416147

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -7.228416147 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -7.228416147 + -2.5
x = -7.228416147 + -2.5

Combine like terms: -7.228416147 + -2.5 = -9.728416147
x = -9.728416147

Simplifying
x = -9.728416147


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.728416147, -9.728416147}
Solution
x = {4.728416147, -9.728416147}

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