x^2+17x-7=0

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Solution for x^2+17x-7=0 equation:


Simplifying
x2 + 17x + -7 = 0

Reorder the terms:
-7 + 17x + x2 = 0

Solving
-7 + 17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 17x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + 17x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 17x + x2 = 0 + 7
17x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
17x + x2 = 7

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 = 7 + 72.25

Reorder the terms:
72.25 + 17x + x2 = 7 + 72.25

Combine like terms: 7 + 72.25 = 79.25
72.25 + 17x + x2 = 79.25

Factor a perfect square on the left side:
(x + 8.5)(x + 8.5) = 79.25

Calculate the square root of the right side: 8.902246907

Break this problem into two subproblems by setting 
(x + 8.5) equal to 8.902246907 and -8.902246907.


Subproblem 1
x + 8.5 = 8.902246907

Simplifying
x + 8.5 = 8.902246907

Reorder the terms:
8.5 + x = 8.902246907

Solving
8.5 + x = 8.902246907

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 = 8.902246907 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = 8.902246907 + -8.5
x = 8.902246907 + -8.5

Combine like terms: 8.902246907 + -8.5 = 0.402246907
x = 0.402246907

Simplifying
x = 0.402246907


Subproblem 2
x + 8.5 = -8.902246907

Simplifying
x + 8.5 = -8.902246907

Reorder the terms:
8.5 + x = -8.902246907

Solving
8.5 + x = -8.902246907

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 = -8.902246907 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + x = -8.902246907 + -8.5
x = -8.902246907 + -8.5

Combine like terms: -8.902246907 + -8.5 = -17.402246907
x = -17.402246907

Simplifying
x = -17.402246907


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.402246907, -17.402246907}

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