x^2+29x+17=

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Solution for x^2+29x+17= equation:


Simplifying
x2 + 29x + 17 = 0

Reorder the terms:
17 + 29x + x2 = 0

Solving
17 + 29x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + 29x + -17 + x2 = 0 + -17

Reorder the terms:
17 + -17 + 29x + x2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 29x + x2 = 0 + -17
29x + x2 = 0 + -17

Combine like terms: 0 + -17 = -17
29x + x2 = -17

The x term is 29x.  Take half its coefficient (14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
29x + 210.25 + x2 = -17 + 210.25

Reorder the terms:
210.25 + 29x + x2 = -17 + 210.25

Combine like terms: -17 + 210.25 = 193.25
210.25 + 29x + x2 = 193.25

Factor a perfect square on the left side:
(x + 14.5)(x + 14.5) = 193.25

Calculate the square root of the right side: 13.901438774

Break this problem into two subproblems by setting 
(x + 14.5) equal to 13.901438774 and -13.901438774.

Subproblem 1

x + 14.5 = 13.901438774 Simplifying x + 14.5 = 13.901438774 Reorder the terms: 14.5 + x = 13.901438774 Solving 14.5 + x = 13.901438774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = 13.901438774 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = 13.901438774 + -14.5 x = 13.901438774 + -14.5 Combine like terms: 13.901438774 + -14.5 = -0.598561226 x = -0.598561226 Simplifying x = -0.598561226

Subproblem 2

x + 14.5 = -13.901438774 Simplifying x + 14.5 = -13.901438774 Reorder the terms: 14.5 + x = -13.901438774 Solving 14.5 + x = -13.901438774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-14.5' to each side of the equation. 14.5 + -14.5 + x = -13.901438774 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + x = -13.901438774 + -14.5 x = -13.901438774 + -14.5 Combine like terms: -13.901438774 + -14.5 = -28.401438774 x = -28.401438774 Simplifying x = -28.401438774

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.598561226, -28.401438774}

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