x^2-34x-322=0

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Solution for x^2-34x-322=0 equation:


Simplifying
x2 + -34x + -322 = 0

Reorder the terms:
-322 + -34x + x2 = 0

Solving
-322 + -34x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '322' to each side of the equation.
-322 + -34x + 322 + x2 = 0 + 322

Reorder the terms:
-322 + 322 + -34x + x2 = 0 + 322

Combine like terms: -322 + 322 = 0
0 + -34x + x2 = 0 + 322
-34x + x2 = 0 + 322

Combine like terms: 0 + 322 = 322
-34x + x2 = 322

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 = 322 + 289

Reorder the terms:
289 + -34x + x2 = 322 + 289

Combine like terms: 322 + 289 = 611
289 + -34x + x2 = 611

Factor a perfect square on the left side:
(x + -17)(x + -17) = 611

Calculate the square root of the right side: 24.718414189

Break this problem into two subproblems by setting 
(x + -17) equal to 24.718414189 and -24.718414189.

Subproblem 1

x + -17 = 24.718414189 Simplifying x + -17 = 24.718414189 Reorder the terms: -17 + x = 24.718414189 Solving -17 + x = 24.718414189 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 = 24.718414189 + 17 Combine like terms: -17 + 17 = 0 0 + x = 24.718414189 + 17 x = 24.718414189 + 17 Combine like terms: 24.718414189 + 17 = 41.718414189 x = 41.718414189 Simplifying x = 41.718414189

Subproblem 2

x + -17 = -24.718414189 Simplifying x + -17 = -24.718414189 Reorder the terms: -17 + x = -24.718414189 Solving -17 + x = -24.718414189 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 = -24.718414189 + 17 Combine like terms: -17 + 17 = 0 0 + x = -24.718414189 + 17 x = -24.718414189 + 17 Combine like terms: -24.718414189 + 17 = -7.718414189 x = -7.718414189 Simplifying x = -7.718414189

Solution

The solution to the problem is based on the solutions from the subproblems. x = {41.718414189, -7.718414189}

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