x^2+34x+24=0

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Solution for x^2+34x+24=0 equation: 


Simplifying
x2 + 34x + 24 = 0

Reorder the terms:
24 + 34x + x2 = 0

Solving
24 + 34x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + 34x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + 34x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + 34x + x2 = 0 + -24
34x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
34x + x2 = -24

The x term is 34x.  Take half its coefficient (17).
Square it (289) and add it to both sides.

Add '289' to each side of the equation.
34x + 289 + x2 = -24 + 289

Reorder the terms:
289 + 34x + x2 = -24 + 289

Combine like terms: -24 + 289 = 265
289 + 34x + x2 = 265

Factor a perfect square on the left side:
(x + 17)(x + 17) = 265

Calculate the square root of the right side: 16.278820596

Break this problem into two subproblems by setting 
(x + 17) equal to 16.278820596 and -16.278820596.


Subproblem 1
x + 17 = 16.278820596

Simplifying
x + 17 = 16.278820596

Reorder the terms:
17 + x = 16.278820596

Solving
17 + x = 16.278820596

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-17' to each side of the equation.
17 + -17 + x = 16.278820596 + -17

Combine like terms: 17 + -17 = 0
0 + x = 16.278820596 + -17
x = 16.278820596 + -17

Combine like terms: 16.278820596 + -17 = -0.721179404
x = -0.721179404

Simplifying
x = -0.721179404


Subproblem 2
x + 17 = -16.278820596

Simplifying
x + 17 = -16.278820596

Reorder the terms:
17 + x = -16.278820596

Solving
17 + x = -16.278820596

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-17' to each side of the equation.
17 + -17 + x = -16.278820596 + -17

Combine like terms: 17 + -17 = 0
0 + x = -16.278820596 + -17
x = -16.278820596 + -17

Combine like terms: -16.278820596 + -17 = -33.278820596
x = -33.278820596

Simplifying
x = -33.278820596


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.721179404, -33.278820596}

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