x^2-17x-2=0

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Solution for x^2-17x-2=0 equation:


Simplifying
x2 + -17x + -2 = 0

Reorder the terms:
-2 + -17x + x2 = 0

Solving
-2 + -17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -17x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -17x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -17x + x2 = 0 + 2
-17x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-17x + x2 = 2

The x term is -17x.  Take half its coefficient (-8.5).
Square it (72.25) and add it to both sides.

Add '72.25' to each side of the equation.
-17x + 72.25 + x2 = 2 + 72.25

Reorder the terms:
72.25 + -17x + x2 = 2 + 72.25

Combine like terms: 2 + 72.25 = 74.25
72.25 + -17x + x2 = 74.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 74.25

Calculate the square root of the right side: 8.61684397

Break this problem into two subproblems by setting 
(x + -8.5) equal to 8.61684397 and -8.61684397.

Subproblem 1

x + -8.5 = 8.61684397 Simplifying x + -8.5 = 8.61684397 Reorder the terms: -8.5 + x = 8.61684397 Solving -8.5 + x = 8.61684397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = 8.61684397 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 8.61684397 + 8.5 x = 8.61684397 + 8.5 Combine like terms: 8.61684397 + 8.5 = 17.11684397 x = 17.11684397 Simplifying x = 17.11684397

Subproblem 2

x + -8.5 = -8.61684397 Simplifying x + -8.5 = -8.61684397 Reorder the terms: -8.5 + x = -8.61684397 Solving -8.5 + x = -8.61684397 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x = -8.61684397 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -8.61684397 + 8.5 x = -8.61684397 + 8.5 Combine like terms: -8.61684397 + 8.5 = -0.11684397 x = -0.11684397 Simplifying x = -0.11684397

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.11684397, -0.11684397}

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