x^2-34x+255=0

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Solution for x^2-34x+255=0 equation:


Simplifying
x2 + -34x + 255 = 0

Reorder the terms:
255 + -34x + x2 = 0

Solving
255 + -34x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-255' to each side of the equation.
255 + -34x + -255 + x2 = 0 + -255

Reorder the terms:
255 + -255 + -34x + x2 = 0 + -255

Combine like terms: 255 + -255 = 0
0 + -34x + x2 = 0 + -255
-34x + x2 = 0 + -255

Combine like terms: 0 + -255 = -255
-34x + x2 = -255

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 = -255 + 289

Reorder the terms:
289 + -34x + x2 = -255 + 289

Combine like terms: -255 + 289 = 34
289 + -34x + x2 = 34

Factor a perfect square on the left side:
(x + -17)(x + -17) = 34

Calculate the square root of the right side: 5.830951895

Break this problem into two subproblems by setting 
(x + -17) equal to 5.830951895 and -5.830951895.

Subproblem 1

x + -17 = 5.830951895 Simplifying x + -17 = 5.830951895 Reorder the terms: -17 + x = 5.830951895 Solving -17 + x = 5.830951895 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 = 5.830951895 + 17 Combine like terms: -17 + 17 = 0 0 + x = 5.830951895 + 17 x = 5.830951895 + 17 Combine like terms: 5.830951895 + 17 = 22.830951895 x = 22.830951895 Simplifying x = 22.830951895

Subproblem 2

x + -17 = -5.830951895 Simplifying x + -17 = -5.830951895 Reorder the terms: -17 + x = -5.830951895 Solving -17 + x = -5.830951895 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 = -5.830951895 + 17 Combine like terms: -17 + 17 = 0 0 + x = -5.830951895 + 17 x = -5.830951895 + 17 Combine like terms: -5.830951895 + 17 = 11.169048105 x = 11.169048105 Simplifying x = 11.169048105

Solution

The solution to the problem is based on the solutions from the subproblems. x = {22.830951895, 11.169048105}

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