3x^2+30x-78=0

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Solution for 3x^2+30x-78=0 equation: 


Simplifying
3x2 + 30x + -78 = 0

Reorder the terms:
-78 + 30x + 3x2 = 0

Solving
-78 + 30x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-26 + 10x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-26 + 10x + x2)' equal to zero and attempt to solve:

Simplifying
-26 + 10x + x2 = 0

Solving
-26 + 10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '26' to each side of the equation.
-26 + 10x + 26 + x2 = 0 + 26

Reorder the terms:
-26 + 26 + 10x + x2 = 0 + 26

Combine like terms: -26 + 26 = 0
0 + 10x + x2 = 0 + 26
10x + x2 = 0 + 26

Combine like terms: 0 + 26 = 26
10x + x2 = 26

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 26 + 25

Reorder the terms:
25 + 10x + x2 = 26 + 25

Combine like terms: 26 + 25 = 51
25 + 10x + x2 = 51

Factor a perfect square on the left side:
(x + 5)(x + 5) = 51

Calculate the square root of the right side: 7.141428429

Break this problem into two subproblems by setting 
(x + 5) equal to 7.141428429 and -7.141428429.


Subproblem 1
x + 5 = 7.141428429

Simplifying
x + 5 = 7.141428429

Reorder the terms:
5 + x = 7.141428429

Solving
5 + x = 7.141428429

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 7.141428429 + -5

Combine like terms: 5 + -5 = 0
0 + x = 7.141428429 + -5
x = 7.141428429 + -5

Combine like terms: 7.141428429 + -5 = 2.141428429
x = 2.141428429

Simplifying
x = 2.141428429


Subproblem 2
x + 5 = -7.141428429

Simplifying
x + 5 = -7.141428429

Reorder the terms:
5 + x = -7.141428429

Solving
5 + x = -7.141428429

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -7.141428429 + -5

Combine like terms: 5 + -5 = 0
0 + x = -7.141428429 + -5
x = -7.141428429 + -5

Combine like terms: -7.141428429 + -5 = -12.141428429
x = -12.141428429

Simplifying
x = -12.141428429


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.141428429, -12.141428429}
Solution
x = {2.141428429, -12.141428429}

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