x^2-34x-289=0

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Solution for x^2-34x-289=0 equation:


Simplifying
x2 + -34x + -289 = 0

Reorder the terms:
-289 + -34x + x2 = 0

Solving
-289 + -34x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '289' to each side of the equation.
-289 + -34x + 289 + x2 = 0 + 289

Reorder the terms:
-289 + 289 + -34x + x2 = 0 + 289

Combine like terms: -289 + 289 = 0
0 + -34x + x2 = 0 + 289
-34x + x2 = 0 + 289

Combine like terms: 0 + 289 = 289
-34x + x2 = 289

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 = 289 + 289

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

Combine like terms: 289 + 289 = 578
289 + -34x + x2 = 578

Factor a perfect square on the left side:
(x + -17)(x + -17) = 578

Calculate the square root of the right side: 24.04163056

Break this problem into two subproblems by setting 
(x + -17) equal to 24.04163056 and -24.04163056.

Subproblem 1

x + -17 = 24.04163056 Simplifying x + -17 = 24.04163056 Reorder the terms: -17 + x = 24.04163056 Solving -17 + x = 24.04163056 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 = 24.04163056 + 17 Combine like terms: -17 + 17 = 0 0 + x = 24.04163056 + 17 x = 24.04163056 + 17 Combine like terms: 24.04163056 + 17 = 41.04163056 x = 41.04163056 Simplifying x = 41.04163056

Subproblem 2

x + -17 = -24.04163056 Simplifying x + -17 = -24.04163056 Reorder the terms: -17 + x = -24.04163056 Solving -17 + x = -24.04163056 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 = -24.04163056 + 17 Combine like terms: -17 + 17 = 0 0 + x = -24.04163056 + 17 x = -24.04163056 + 17 Combine like terms: -24.04163056 + 17 = -7.04163056 x = -7.04163056 Simplifying x = -7.04163056

Solution

The solution to the problem is based on the solutions from the subproblems. x = {41.04163056, -7.04163056}

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