x^2-7x-38=0

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


Simplifying
x2 + -7x + -38 = 0

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

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

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

Combine like terms: -38 + 38 = 0
0 + -7x + x2 = 0 + 38
-7x + x2 = 0 + 38

Combine like terms: 0 + 38 = 38
-7x + x2 = 38

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 38 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 38 + 12.25

Combine like terms: 38 + 12.25 = 50.25
12.25 + -7x + x2 = 50.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 50.25

Calculate the square root of the right side: 7.088723439

Break this problem into two subproblems by setting 
(x + -3.5) equal to 7.088723439 and -7.088723439.


Subproblem 1
x + -3.5 = 7.088723439

Simplifying
x + -3.5 = 7.088723439

Reorder the terms:
-3.5 + x = 7.088723439

Solving
-3.5 + x = 7.088723439

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 7.088723439 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 7.088723439 + 3.5
x = 7.088723439 + 3.5

Combine like terms: 7.088723439 + 3.5 = 10.588723439
x = 10.588723439

Simplifying
x = 10.588723439


Subproblem 2
x + -3.5 = -7.088723439

Simplifying
x + -3.5 = -7.088723439

Reorder the terms:
-3.5 + x = -7.088723439

Solving
-3.5 + x = -7.088723439

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -7.088723439 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -7.088723439 + 3.5
x = -7.088723439 + 3.5

Combine like terms: -7.088723439 + 3.5 = -3.588723439
x = -3.588723439

Simplifying
x = -3.588723439


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.588723439, -3.588723439}

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