x*x-17x-17=0

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Solution for x*x-17x-17=0 equation:


Simplifying
x * x + -17x + -17 = 0

Multiply x * x
x2 + -17x + -17 = 0

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

Solving
-17 + -17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 17 + 72.25

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

Combine like terms: 17 + 72.25 = 89.25
72.25 + -17x + x2 = 89.25

Factor a perfect square on the left side:
(x + -8.5)(x + -8.5) = 89.25

Calculate the square root of the right side: 9.447221814

Break this problem into two subproblems by setting 
(x + -8.5) equal to 9.447221814 and -9.447221814.

Subproblem 1

x + -8.5 = 9.447221814 Simplifying x + -8.5 = 9.447221814 Reorder the terms: -8.5 + x = 9.447221814 Solving -8.5 + x = 9.447221814 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 = 9.447221814 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = 9.447221814 + 8.5 x = 9.447221814 + 8.5 Combine like terms: 9.447221814 + 8.5 = 17.947221814 x = 17.947221814 Simplifying x = 17.947221814

Subproblem 2

x + -8.5 = -9.447221814 Simplifying x + -8.5 = -9.447221814 Reorder the terms: -8.5 + x = -9.447221814 Solving -8.5 + x = -9.447221814 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 = -9.447221814 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x = -9.447221814 + 8.5 x = -9.447221814 + 8.5 Combine like terms: -9.447221814 + 8.5 = -0.947221814 x = -0.947221814 Simplifying x = -0.947221814

Solution

The solution to the problem is based on the solutions from the subproblems. x = {17.947221814, -0.947221814}

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