x^2+13x-38=0

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Solution for x^2+13x-38=0 equation:


Simplifying
x2 + 13x + -38 = 0

Reorder the terms:
-38 + 13x + x2 = 0

Solving
-38 + 13x + 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 + 13x + 38 + x2 = 0 + 38

Reorder the terms:
-38 + 38 + 13x + x2 = 0 + 38

Combine like terms: -38 + 38 = 0
0 + 13x + x2 = 0 + 38
13x + x2 = 0 + 38

Combine like terms: 0 + 38 = 38
13x + x2 = 38

The x term is 13x.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13x + 42.25 + x2 = 38 + 42.25

Reorder the terms:
42.25 + 13x + x2 = 38 + 42.25

Combine like terms: 38 + 42.25 = 80.25
42.25 + 13x + x2 = 80.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 80.25

Calculate the square root of the right side: 8.958236434

Break this problem into two subproblems by setting 
(x + 6.5) equal to 8.958236434 and -8.958236434.

Subproblem 1

x + 6.5 = 8.958236434 Simplifying x + 6.5 = 8.958236434 Reorder the terms: 6.5 + x = 8.958236434 Solving 6.5 + x = 8.958236434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 8.958236434 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 8.958236434 + -6.5 x = 8.958236434 + -6.5 Combine like terms: 8.958236434 + -6.5 = 2.458236434 x = 2.458236434 Simplifying x = 2.458236434

Subproblem 2

x + 6.5 = -8.958236434 Simplifying x + 6.5 = -8.958236434 Reorder the terms: 6.5 + x = -8.958236434 Solving 6.5 + x = -8.958236434 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -8.958236434 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -8.958236434 + -6.5 x = -8.958236434 + -6.5 Combine like terms: -8.958236434 + -6.5 = -15.458236434 x = -15.458236434 Simplifying x = -15.458236434

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.458236434, -15.458236434}

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