x^2+5x-175=0

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Solution for x^2+5x-175=0 equation: 


Simplifying
x2 + 5x + -175 = 0

Reorder the terms:
-175 + 5x + x2 = 0

Solving
-175 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '175' to each side of the equation.
-175 + 5x + 175 + x2 = 0 + 175

Reorder the terms:
-175 + 175 + 5x + x2 = 0 + 175

Combine like terms: -175 + 175 = 0
0 + 5x + x2 = 0 + 175
5x + x2 = 0 + 175

Combine like terms: 0 + 175 = 175
5x + x2 = 175

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 175 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 175 + 6.25

Combine like terms: 175 + 6.25 = 181.25
6.25 + 5x + x2 = 181.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 181.25

Calculate the square root of the right side: 13.462912018

Break this problem into two subproblems by setting 
(x + 2.5) equal to 13.462912018 and -13.462912018.


Subproblem 1
x + 2.5 = 13.462912018

Simplifying
x + 2.5 = 13.462912018

Reorder the terms:
2.5 + x = 13.462912018

Solving
2.5 + x = 13.462912018

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 13.462912018 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 13.462912018 + -2.5
x = 13.462912018 + -2.5

Combine like terms: 13.462912018 + -2.5 = 10.962912018
x = 10.962912018

Simplifying
x = 10.962912018


Subproblem 2
x + 2.5 = -13.462912018

Simplifying
x + 2.5 = -13.462912018

Reorder the terms:
2.5 + x = -13.462912018

Solving
2.5 + x = -13.462912018

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -13.462912018 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -13.462912018 + -2.5
x = -13.462912018 + -2.5

Combine like terms: -13.462912018 + -2.5 = -15.962912018
x = -15.962912018

Simplifying
x = -15.962912018


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.962912018, -15.962912018}

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