x^2+28x+2=0

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Solution for x^2+28x+2=0 equation:


Simplifying
x2 + 28x + 2 = 0

Reorder the terms:
2 + 28x + x2 = 0

Solving
2 + 28x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 28x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 28x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 28x + x2 = 0 + -2
28x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
28x + x2 = -2

The x term is 28x.  Take half its coefficient (14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
28x + 196 + x2 = -2 + 196

Reorder the terms:
196 + 28x + x2 = -2 + 196

Combine like terms: -2 + 196 = 194
196 + 28x + x2 = 194

Factor a perfect square on the left side:
(x + 14)(x + 14) = 194

Calculate the square root of the right side: 13.928388277

Break this problem into two subproblems by setting 
(x + 14) equal to 13.928388277 and -13.928388277.

Subproblem 1

x + 14 = 13.928388277 Simplifying x + 14 = 13.928388277 Reorder the terms: 14 + x = 13.928388277 Solving 14 + x = 13.928388277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 13.928388277 + -14 Combine like terms: 14 + -14 = 0 0 + x = 13.928388277 + -14 x = 13.928388277 + -14 Combine like terms: 13.928388277 + -14 = -0.071611723 x = -0.071611723 Simplifying x = -0.071611723

Subproblem 2

x + 14 = -13.928388277 Simplifying x + 14 = -13.928388277 Reorder the terms: 14 + x = -13.928388277 Solving 14 + x = -13.928388277 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = -13.928388277 + -14 Combine like terms: 14 + -14 = 0 0 + x = -13.928388277 + -14 x = -13.928388277 + -14 Combine like terms: -13.928388277 + -14 = -27.928388277 x = -27.928388277 Simplifying x = -27.928388277

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.071611723, -27.928388277}

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