x^2+5x-174=0

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Solution for x^2+5x-174=0 equation: 


Simplifying
x2 + 5x + -174 = 0

Reorder the terms:
-174 + 5x + x2 = 0

Solving
-174 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '174' to each side of the equation.
-174 + 5x + 174 + x2 = 0 + 174

Reorder the terms:
-174 + 174 + 5x + x2 = 0 + 174

Combine like terms: -174 + 174 = 0
0 + 5x + x2 = 0 + 174
5x + x2 = 0 + 174

Combine like terms: 0 + 174 = 174
5x + x2 = 174

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 = 174 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 174 + 6.25

Combine like terms: 174 + 6.25 = 180.25
6.25 + 5x + x2 = 180.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 180.25

Calculate the square root of the right side: 13.425721582

Break this problem into two subproblems by setting 
(x + 2.5) equal to 13.425721582 and -13.425721582.


Subproblem 1
x + 2.5 = 13.425721582

Simplifying
x + 2.5 = 13.425721582

Reorder the terms:
2.5 + x = 13.425721582

Solving
2.5 + x = 13.425721582

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 = 13.425721582 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 13.425721582 + -2.5
x = 13.425721582 + -2.5

Combine like terms: 13.425721582 + -2.5 = 10.925721582
x = 10.925721582

Simplifying
x = 10.925721582


Subproblem 2
x + 2.5 = -13.425721582

Simplifying
x + 2.5 = -13.425721582

Reorder the terms:
2.5 + x = -13.425721582

Solving
2.5 + x = -13.425721582

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 = -13.425721582 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -13.425721582 + -2.5
x = -13.425721582 + -2.5

Combine like terms: -13.425721582 + -2.5 = -15.925721582
x = -15.925721582

Simplifying
x = -15.925721582


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.925721582, -15.925721582}

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