x^2+14x=-39

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Solution for x^2+14x=-39 equation:


Simplifying
x2 + 14x = -39

Reorder the terms:
14x + x2 = -39

Solving
14x + x2 = -39

Solving for variable 'x'.

Reorder the terms:
39 + 14x + x2 = -39 + 39

Combine like terms: -39 + 39 = 0
39 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-39' to each side of the equation.
39 + 14x + -39 + x2 = 0 + -39

Reorder the terms:
39 + -39 + 14x + x2 = 0 + -39

Combine like terms: 39 + -39 = 0
0 + 14x + x2 = 0 + -39
14x + x2 = 0 + -39

Combine like terms: 0 + -39 = -39
14x + x2 = -39

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -39 + 49

Reorder the terms:
49 + 14x + x2 = -39 + 49

Combine like terms: -39 + 49 = 10
49 + 14x + x2 = 10

Factor a perfect square on the left side:
(x + 7)(x + 7) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(x + 7) equal to 3.16227766 and -3.16227766.

Subproblem 1

x + 7 = 3.16227766 Simplifying x + 7 = 3.16227766 Reorder the terms: 7 + x = 3.16227766 Solving 7 + x = 3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 3.16227766 + -7 Combine like terms: 7 + -7 = 0 0 + x = 3.16227766 + -7 x = 3.16227766 + -7 Combine like terms: 3.16227766 + -7 = -3.83772234 x = -3.83772234 Simplifying x = -3.83772234

Subproblem 2

x + 7 = -3.16227766 Simplifying x + 7 = -3.16227766 Reorder the terms: 7 + x = -3.16227766 Solving 7 + x = -3.16227766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = -3.16227766 + -7 Combine like terms: 7 + -7 = 0 0 + x = -3.16227766 + -7 x = -3.16227766 + -7 Combine like terms: -3.16227766 + -7 = -10.16227766 x = -10.16227766 Simplifying x = -10.16227766

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-3.83772234, -10.16227766}

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