(x^2-34x-136)=0

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Solution for (x^2-34x-136)=0 equation: 


Simplifying
(x2 + -34x + -136) = 0

Reorder the terms:
(-136 + -34x + x2) = 0

Remove parenthesis around (-136 + -34x + x2)
-136 + -34x + x2 = 0

Solving
-136 + -34x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '136' to each side of the equation.
-136 + -34x + 136 + x2 = 0 + 136

Reorder the terms:
-136 + 136 + -34x + x2 = 0 + 136

Combine like terms: -136 + 136 = 0
0 + -34x + x2 = 0 + 136
-34x + x2 = 0 + 136

Combine like terms: 0 + 136 = 136
-34x + x2 = 136

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 = 136 + 289

Reorder the terms:
289 + -34x + x2 = 136 + 289

Combine like terms: 136 + 289 = 425
289 + -34x + x2 = 425

Factor a perfect square on the left side:
(x + -17)(x + -17) = 425

Calculate the square root of the right side: 20.615528128

Break this problem into two subproblems by setting 
(x + -17) equal to 20.615528128 and -20.615528128.


Subproblem 1
x + -17 = 20.615528128

Simplifying
x + -17 = 20.615528128

Reorder the terms:
-17 + x = 20.615528128

Solving
-17 + x = 20.615528128

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 = 20.615528128 + 17

Combine like terms: -17 + 17 = 0
0 + x = 20.615528128 + 17
x = 20.615528128 + 17

Combine like terms: 20.615528128 + 17 = 37.615528128
x = 37.615528128

Simplifying
x = 37.615528128


Subproblem 2
x + -17 = -20.615528128

Simplifying
x + -17 = -20.615528128

Reorder the terms:
-17 + x = -20.615528128

Solving
-17 + x = -20.615528128

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 = -20.615528128 + 17

Combine like terms: -17 + 17 = 0
0 + x = -20.615528128 + 17
x = -20.615528128 + 17

Combine like terms: -20.615528128 + 17 = -3.615528128
x = -3.615528128

Simplifying
x = -3.615528128


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {37.615528128, -3.615528128}

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