x^2+34x-367=0

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Solution for x^2+34x-367=0 equation: 


Simplifying
x2 + 34x + -367 = 0

Reorder the terms:
-367 + 34x + x2 = 0

Solving
-367 + 34x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '367' to each side of the equation.
-367 + 34x + 367 + x2 = 0 + 367

Reorder the terms:
-367 + 367 + 34x + x2 = 0 + 367

Combine like terms: -367 + 367 = 0
0 + 34x + x2 = 0 + 367
34x + x2 = 0 + 367

Combine like terms: 0 + 367 = 367
34x + x2 = 367

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 = 367 + 289

Reorder the terms:
289 + 34x + x2 = 367 + 289

Combine like terms: 367 + 289 = 656
289 + 34x + x2 = 656

Factor a perfect square on the left side:
(x + 17)(x + 17) = 656

Calculate the square root of the right side: 25.61249695

Break this problem into two subproblems by setting 
(x + 17) equal to 25.61249695 and -25.61249695.


Subproblem 1
x + 17 = 25.61249695

Simplifying
x + 17 = 25.61249695

Reorder the terms:
17 + x = 25.61249695

Solving
17 + x = 25.61249695

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 = 25.61249695 + -17

Combine like terms: 17 + -17 = 0
0 + x = 25.61249695 + -17
x = 25.61249695 + -17

Combine like terms: 25.61249695 + -17 = 8.61249695
x = 8.61249695

Simplifying
x = 8.61249695


Subproblem 2
x + 17 = -25.61249695

Simplifying
x + 17 = -25.61249695

Reorder the terms:
17 + x = -25.61249695

Solving
17 + x = -25.61249695

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 = -25.61249695 + -17

Combine like terms: 17 + -17 = 0
0 + x = -25.61249695 + -17
x = -25.61249695 + -17

Combine like terms: -25.61249695 + -17 = -42.61249695
x = -42.61249695

Simplifying
x = -42.61249695


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.61249695, -42.61249695}

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