x^2+8.7x-17.4=0

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Solution for x^2+8.7x-17.4=0 equation: 


Simplifying
x2 + 8.7x + -17.4 = 0

Reorder the terms:
-17.4 + 8.7x + x2 = 0

Solving
-17.4 + 8.7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '17.4' to each side of the equation.
-17.4 + 8.7x + 17.4 + x2 = 0 + 17.4

Reorder the terms:
-17.4 + 17.4 + 8.7x + x2 = 0 + 17.4

Combine like terms: -17.4 + 17.4 = 0.0
0.0 + 8.7x + x2 = 0 + 17.4
8.7x + x2 = 0 + 17.4

Combine like terms: 0 + 17.4 = 17.4
8.7x + x2 = 17.4

The x term is 8.7x.  Take half its coefficient (4.35).
Square it (18.9225) and add it to both sides.

Add '18.9225' to each side of the equation.
8.7x + 18.9225 + x2 = 17.4 + 18.9225

Reorder the terms:
18.9225 + 8.7x + x2 = 17.4 + 18.9225

Combine like terms: 17.4 + 18.9225 = 36.3225
18.9225 + 8.7x + x2 = 36.3225

Factor a perfect square on the left side:
(x + 4.35)(x + 4.35) = 36.3225

Calculate the square root of the right side: 6.026815079

Break this problem into two subproblems by setting 
(x + 4.35) equal to 6.026815079 and -6.026815079.


Subproblem 1
x + 4.35 = 6.026815079

Simplifying
x + 4.35 = 6.026815079

Reorder the terms:
4.35 + x = 6.026815079

Solving
4.35 + x = 6.026815079

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4.35' to each side of the equation.
4.35 + -4.35 + x = 6.026815079 + -4.35

Combine like terms: 4.35 + -4.35 = 0.00
0.00 + x = 6.026815079 + -4.35
x = 6.026815079 + -4.35

Combine like terms: 6.026815079 + -4.35 = 1.676815079
x = 1.676815079

Simplifying
x = 1.676815079


Subproblem 2
x + 4.35 = -6.026815079

Simplifying
x + 4.35 = -6.026815079

Reorder the terms:
4.35 + x = -6.026815079

Solving
4.35 + x = -6.026815079

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-4.35' to each side of the equation.
4.35 + -4.35 + x = -6.026815079 + -4.35

Combine like terms: 4.35 + -4.35 = 0.00
0.00 + x = -6.026815079 + -4.35
x = -6.026815079 + -4.35

Combine like terms: -6.026815079 + -4.35 = -10.376815079
x = -10.376815079

Simplifying
x = -10.376815079


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.676815079, -10.376815079}

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