2x^2-6x-30=0

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Solution for 2x^2-6x-30=0 equation: 


Simplifying
2x2 + -6x + -30 = 0

Reorder the terms:
-30 + -6x + 2x2 = 0

Solving
-30 + -6x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
-15 + -3x + x2 = 0

Solving
-15 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -3x + 15 + x2 = 0 + 15

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

Combine like terms: -15 + 15 = 0
0 + -3x + x2 = 0 + 15
-3x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-3x + x2 = 15

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 15 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 15 + 2.25

Combine like terms: 15 + 2.25 = 17.25
2.25 + -3x + x2 = 17.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(x + -1.5) equal to 4.153311931 and -4.153311931.


Subproblem 1
x + -1.5 = 4.153311931

Simplifying
x + -1.5 = 4.153311931

Reorder the terms:
-1.5 + x = 4.153311931

Solving
-1.5 + x = 4.153311931

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 4.153311931 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 4.153311931 + 1.5
x = 4.153311931 + 1.5

Combine like terms: 4.153311931 + 1.5 = 5.653311931
x = 5.653311931

Simplifying
x = 5.653311931


Subproblem 2
x + -1.5 = -4.153311931

Simplifying
x + -1.5 = -4.153311931

Reorder the terms:
-1.5 + x = -4.153311931

Solving
-1.5 + x = -4.153311931

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -4.153311931 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -4.153311931 + 1.5
x = -4.153311931 + 1.5

Combine like terms: -4.153311931 + 1.5 = -2.653311931
x = -2.653311931

Simplifying
x = -2.653311931


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.653311931, -2.653311931}
Solution
x = {5.653311931, -2.653311931}

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