2x^2+38x+102=0

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Solution for 2x^2+38x+102=0 equation: 


Simplifying
2x2 + 38x + 102 = 0

Reorder the terms:
102 + 38x + 2x2 = 0

Solving
102 + 38x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(51 + 19x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(51 + 19x + x2)' equal to zero and attempt to solve:

Simplifying
51 + 19x + x2 = 0

Solving
51 + 19x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-51' to each side of the equation.
51 + 19x + -51 + x2 = 0 + -51

Reorder the terms:
51 + -51 + 19x + x2 = 0 + -51

Combine like terms: 51 + -51 = 0
0 + 19x + x2 = 0 + -51
19x + x2 = 0 + -51

Combine like terms: 0 + -51 = -51
19x + x2 = -51

The x term is 19x.  Take half its coefficient (9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
19x + 90.25 + x2 = -51 + 90.25

Reorder the terms:
90.25 + 19x + x2 = -51 + 90.25

Combine like terms: -51 + 90.25 = 39.25
90.25 + 19x + x2 = 39.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 39.25

Calculate the square root of the right side: 6.264982043

Break this problem into two subproblems by setting 
(x + 9.5) equal to 6.264982043 and -6.264982043.


Subproblem 1
x + 9.5 = 6.264982043

Simplifying
x + 9.5 = 6.264982043

Reorder the terms:
9.5 + x = 6.264982043

Solving
9.5 + x = 6.264982043

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = 6.264982043 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 6.264982043 + -9.5
x = 6.264982043 + -9.5

Combine like terms: 6.264982043 + -9.5 = -3.235017957
x = -3.235017957

Simplifying
x = -3.235017957


Subproblem 2
x + 9.5 = -6.264982043

Simplifying
x + 9.5 = -6.264982043

Reorder the terms:
9.5 + x = -6.264982043

Solving
9.5 + x = -6.264982043

Solving for variable 'x'.

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

Add '-9.5' to each side of the equation.
9.5 + -9.5 + x = -6.264982043 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = -6.264982043 + -9.5
x = -6.264982043 + -9.5

Combine like terms: -6.264982043 + -9.5 = -15.764982043
x = -15.764982043

Simplifying
x = -15.764982043


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.235017957, -15.764982043}
Solution
x = {-3.235017957, -15.764982043}

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