x(2x+38)=10

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Solution for x(2x+38)=10 equation: 


Simplifying
x(2x + 38) = 10

Reorder the terms:
x(38 + 2x) = 10
(38 * x + 2x * x) = 10
(38x + 2x2) = 10

Solving
38x + 2x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 38x + 2x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 38x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 19x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 19x + x2)' equal to zero and attempt to solve:

Simplifying
-5 + 19x + x2 = 0

Solving
-5 + 19x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 19x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 19x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 19x + x2 = 0 + 5
19x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
19x + x2 = 5

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 = 5 + 90.25

Reorder the terms:
90.25 + 19x + x2 = 5 + 90.25

Combine like terms: 5 + 90.25 = 95.25
90.25 + 19x + x2 = 95.25

Factor a perfect square on the left side:
(x + 9.5)(x + 9.5) = 95.25

Calculate the square root of the right side: 9.759610648

Break this problem into two subproblems by setting 
(x + 9.5) equal to 9.759610648 and -9.759610648.


Subproblem 1
x + 9.5 = 9.759610648

Simplifying
x + 9.5 = 9.759610648

Reorder the terms:
9.5 + x = 9.759610648

Solving
9.5 + x = 9.759610648

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 = 9.759610648 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = 9.759610648 + -9.5
x = 9.759610648 + -9.5

Combine like terms: 9.759610648 + -9.5 = 0.259610648
x = 0.259610648

Simplifying
x = 0.259610648


Subproblem 2
x + 9.5 = -9.759610648

Simplifying
x + 9.5 = -9.759610648

Reorder the terms:
9.5 + x = -9.759610648

Solving
9.5 + x = -9.759610648

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 = -9.759610648 + -9.5

Combine like terms: 9.5 + -9.5 = 0.0
0.0 + x = -9.759610648 + -9.5
x = -9.759610648 + -9.5

Combine like terms: -9.759610648 + -9.5 = -19.259610648
x = -19.259610648

Simplifying
x = -19.259610648


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.259610648, -19.259610648}
Solution
x = {0.259610648, -19.259610648}

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