x^2+28x+29=

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Solution for x^2+28x+29= equation:


Simplifying
x2 + 28x + 29 = 0

Reorder the terms:
29 + 28x + x2 = 0

Solving
29 + 28x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-29' to each side of the equation.
29 + 28x + -29 + x2 = 0 + -29

Reorder the terms:
29 + -29 + 28x + x2 = 0 + -29

Combine like terms: 29 + -29 = 0
0 + 28x + x2 = 0 + -29
28x + x2 = 0 + -29

Combine like terms: 0 + -29 = -29
28x + x2 = -29

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 = -29 + 196

Reorder the terms:
196 + 28x + x2 = -29 + 196

Combine like terms: -29 + 196 = 167
196 + 28x + x2 = 167

Factor a perfect square on the left side:
(x + 14)(x + 14) = 167

Calculate the square root of the right side: 12.922847983

Break this problem into two subproblems by setting 
(x + 14) equal to 12.922847983 and -12.922847983.

Subproblem 1

x + 14 = 12.922847983 Simplifying x + 14 = 12.922847983 Reorder the terms: 14 + x = 12.922847983 Solving 14 + x = 12.922847983 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 = 12.922847983 + -14 Combine like terms: 14 + -14 = 0 0 + x = 12.922847983 + -14 x = 12.922847983 + -14 Combine like terms: 12.922847983 + -14 = -1.077152017 x = -1.077152017 Simplifying x = -1.077152017

Subproblem 2

x + 14 = -12.922847983 Simplifying x + 14 = -12.922847983 Reorder the terms: 14 + x = -12.922847983 Solving 14 + x = -12.922847983 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 = -12.922847983 + -14 Combine like terms: 14 + -14 = 0 0 + x = -12.922847983 + -14 x = -12.922847983 + -14 Combine like terms: -12.922847983 + -14 = -26.922847983 x = -26.922847983 Simplifying x = -26.922847983

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.077152017, -26.922847983}

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