x(x)+14x=-2

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Solution for x(x)+14x=-2 equation:


Simplifying
x(x) + 14x = -2

Multiply x * x
x2 + 14x = -2

Reorder the terms:
14x + x2 = -2

Solving
14x + x2 = -2

Solving for variable 'x'.

Reorder the terms:
2 + 14x + x2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 14x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 14x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 14x + x2 = 0 + -2
14x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
14x + x2 = -2

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 = -2 + 49

Reorder the terms:
49 + 14x + x2 = -2 + 49

Combine like terms: -2 + 49 = 47
49 + 14x + x2 = 47

Factor a perfect square on the left side:
(x + 7)(x + 7) = 47

Calculate the square root of the right side: 6.8556546

Break this problem into two subproblems by setting 
(x + 7) equal to 6.8556546 and -6.8556546.

Subproblem 1

x + 7 = 6.8556546 Simplifying x + 7 = 6.8556546 Reorder the terms: 7 + x = 6.8556546 Solving 7 + x = 6.8556546 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 = 6.8556546 + -7 Combine like terms: 7 + -7 = 0 0 + x = 6.8556546 + -7 x = 6.8556546 + -7 Combine like terms: 6.8556546 + -7 = -0.1443454 x = -0.1443454 Simplifying x = -0.1443454

Subproblem 2

x + 7 = -6.8556546 Simplifying x + 7 = -6.8556546 Reorder the terms: 7 + x = -6.8556546 Solving 7 + x = -6.8556546 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 = -6.8556546 + -7 Combine like terms: 7 + -7 = 0 0 + x = -6.8556546 + -7 x = -6.8556546 + -7 Combine like terms: -6.8556546 + -7 = -13.8556546 x = -13.8556546 Simplifying x = -13.8556546

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.1443454, -13.8556546}

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