x^2+15x+38=0

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Solution for x^2+15x+38=0 equation:


Simplifying
x2 + 15x + 38 = 0

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

Solving
38 + 15x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-38' to each side of the equation.
38 + 15x + -38 + x2 = 0 + -38

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

Combine like terms: 38 + -38 = 0
0 + 15x + x2 = 0 + -38
15x + x2 = 0 + -38

Combine like terms: 0 + -38 = -38
15x + x2 = -38

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 = -38 + 56.25

Reorder the terms:
56.25 + 15x + x2 = -38 + 56.25

Combine like terms: -38 + 56.25 = 18.25
56.25 + 15x + x2 = 18.25

Factor a perfect square on the left side:
(x + 7.5)(x + 7.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(x + 7.5) equal to 4.272001873 and -4.272001873.

Subproblem 1

x + 7.5 = 4.272001873 Simplifying x + 7.5 = 4.272001873 Reorder the terms: 7.5 + x = 4.272001873 Solving 7.5 + x = 4.272001873 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 = 4.272001873 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 4.272001873 + -7.5 x = 4.272001873 + -7.5 Combine like terms: 4.272001873 + -7.5 = -3.227998127 x = -3.227998127 Simplifying x = -3.227998127

Subproblem 2

x + 7.5 = -4.272001873 Simplifying x + 7.5 = -4.272001873 Reorder the terms: 7.5 + x = -4.272001873 Solving 7.5 + x = -4.272001873 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 = -4.272001873 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -4.272001873 + -7.5 x = -4.272001873 + -7.5 Combine like terms: -4.272001873 + -7.5 = -11.772001873 x = -11.772001873 Simplifying x = -11.772001873

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.227998127, -11.772001873}

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