2x^2+30x-38=0

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Solution for 2x^2+30x-38=0 equation: 


Simplifying
2x2 + 30x + -38 = 0

Reorder the terms:
-38 + 30x + 2x2 = 0

Solving
-38 + 30x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-19 + 15x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-19 + 15x + x2)' equal to zero and attempt to solve:

Simplifying
-19 + 15x + x2 = 0

Solving
-19 + 15x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 15x + 19 + x2 = 0 + 19

Reorder the terms:
-19 + 19 + 15x + x2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 15x + x2 = 0 + 19
15x + x2 = 0 + 19

Combine like terms: 0 + 19 = 19
15x + x2 = 19

The x term is 15x.  Take half its coefficient (7.5).
Square it (56.25) and add it to both sides.

Add '56.25' to each side of the equation.
15x + 56.25 + x2 = 19 + 56.25

Reorder the terms:
56.25 + 15x + x2 = 19 + 56.25

Combine like terms: 19 + 56.25 = 75.25
56.25 + 15x + x2 = 75.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 75.25

Calculate the square root of the right side: 8.674675786

Break this problem into two subproblems by setting 
(x + 7.5) equal to 8.674675786 and -8.674675786.


Subproblem 1
x + 7.5 = 8.674675786

Simplifying
x + 7.5 = 8.674675786

Reorder the terms:
7.5 + x = 8.674675786

Solving
7.5 + x = 8.674675786

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = 8.674675786 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = 8.674675786 + -7.5
x = 8.674675786 + -7.5

Combine like terms: 8.674675786 + -7.5 = 1.174675786
x = 1.174675786

Simplifying
x = 1.174675786


Subproblem 2
x + 7.5 = -8.674675786

Simplifying
x + 7.5 = -8.674675786

Reorder the terms:
7.5 + x = -8.674675786

Solving
7.5 + x = -8.674675786

Solving for variable 'x'.

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

Add '-7.5' to each side of the equation.
7.5 + -7.5 + x = -8.674675786 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + x = -8.674675786 + -7.5
x = -8.674675786 + -7.5

Combine like terms: -8.674675786 + -7.5 = -16.174675786
x = -16.174675786

Simplifying
x = -16.174675786


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.174675786, -16.174675786}
Solution
x = {1.174675786, -16.174675786}

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