x^2+2x+-38=0

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


Simplifying
x2 + 2x + -38 = 0

Reorder the terms:
-38 + 2x + x2 = 0

Solving
-38 + 2x + 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 + 2x + 38 + x2 = 0 + 38

Reorder the terms:
-38 + 38 + 2x + x2 = 0 + 38

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

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

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 38 + 1

Reorder the terms:
1 + 2x + x2 = 38 + 1

Combine like terms: 38 + 1 = 39
1 + 2x + x2 = 39

Factor a perfect square on the left side:
(x + 1)(x + 1) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(x + 1) equal to 6.244997998 and -6.244997998.

Subproblem 1

x + 1 = 6.244997998 Simplifying x + 1 = 6.244997998 Reorder the terms: 1 + x = 6.244997998 Solving 1 + x = 6.244997998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 6.244997998 + -1 Combine like terms: 1 + -1 = 0 0 + x = 6.244997998 + -1 x = 6.244997998 + -1 Combine like terms: 6.244997998 + -1 = 5.244997998 x = 5.244997998 Simplifying x = 5.244997998

Subproblem 2

x + 1 = -6.244997998 Simplifying x + 1 = -6.244997998 Reorder the terms: 1 + x = -6.244997998 Solving 1 + x = -6.244997998 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -6.244997998 + -1 Combine like terms: 1 + -1 = 0 0 + x = -6.244997998 + -1 x = -6.244997998 + -1 Combine like terms: -6.244997998 + -1 = -7.244997998 x = -7.244997998 Simplifying x = -7.244997998

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.244997998, -7.244997998}

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