15x^2-7x-38=0

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Solution for 15x^2-7x-38=0 equation: 


Simplifying
15x2 + -7x + -38 = 0

Reorder the terms:
-38 + -7x + 15x2 = 0

Solving
-38 + -7x + 15x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
15 the coefficient of the squared term: 

Divide each side by '15'.
-2.533333333 + -0.4666666667x + x2 = 0

Move the constant term to the right:

Add '2.533333333' to each side of the equation.
-2.533333333 + -0.4666666667x + 2.533333333 + x2 = 0 + 2.533333333

Reorder the terms:
-2.533333333 + 2.533333333 + -0.4666666667x + x2 = 0 + 2.533333333

Combine like terms: -2.533333333 + 2.533333333 = 0.000000000
0.000000000 + -0.4666666667x + x2 = 0 + 2.533333333
-0.4666666667x + x2 = 0 + 2.533333333

Combine like terms: 0 + 2.533333333 = 2.533333333
-0.4666666667x + x2 = 2.533333333

The x term is -0.4666666667x.  Take half its coefficient (-0.2333333334).
Square it (0.05444444448) and add it to both sides.

Add '0.05444444448' to each side of the equation.
-0.4666666667x + 0.05444444448 + x2 = 2.533333333 + 0.05444444448

Reorder the terms:
0.05444444448 + -0.4666666667x + x2 = 2.533333333 + 0.05444444448

Combine like terms: 2.533333333 + 0.05444444448 = 2.58777777748
0.05444444448 + -0.4666666667x + x2 = 2.58777777748

Factor a perfect square on the left side:
(x + -0.2333333334)(x + -0.2333333334) = 2.58777777748

Calculate the square root of the right side: 1.608657135

Break this problem into two subproblems by setting 
(x + -0.2333333334) equal to 1.608657135 and -1.608657135.


Subproblem 1
x + -0.2333333334 = 1.608657135

Simplifying
x + -0.2333333334 = 1.608657135

Reorder the terms:
-0.2333333334 + x = 1.608657135

Solving
-0.2333333334 + x = 1.608657135

Solving for variable 'x'.

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

Add '0.2333333334' to each side of the equation.
-0.2333333334 + 0.2333333334 + x = 1.608657135 + 0.2333333334

Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000
0.0000000000 + x = 1.608657135 + 0.2333333334
x = 1.608657135 + 0.2333333334

Combine like terms: 1.608657135 + 0.2333333334 = 1.8419904684
x = 1.8419904684

Simplifying
x = 1.8419904684


Subproblem 2
x + -0.2333333334 = -1.608657135

Simplifying
x + -0.2333333334 = -1.608657135

Reorder the terms:
-0.2333333334 + x = -1.608657135

Solving
-0.2333333334 + x = -1.608657135

Solving for variable 'x'.

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

Add '0.2333333334' to each side of the equation.
-0.2333333334 + 0.2333333334 + x = -1.608657135 + 0.2333333334

Combine like terms: -0.2333333334 + 0.2333333334 = 0.0000000000
0.0000000000 + x = -1.608657135 + 0.2333333334
x = -1.608657135 + 0.2333333334

Combine like terms: -1.608657135 + 0.2333333334 = -1.3753238016
x = -1.3753238016

Simplifying
x = -1.3753238016


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.8419904684, -1.3753238016}

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