x^2+5x-246=0

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Solution for x^2+5x-246=0 equation: 


Simplifying
x2 + 5x + -246 = 0

Reorder the terms:
-246 + 5x + x2 = 0

Solving
-246 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '246' to each side of the equation.
-246 + 5x + 246 + x2 = 0 + 246

Reorder the terms:
-246 + 246 + 5x + x2 = 0 + 246

Combine like terms: -246 + 246 = 0
0 + 5x + x2 = 0 + 246
5x + x2 = 0 + 246

Combine like terms: 0 + 246 = 246
5x + x2 = 246

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 = 246 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 246 + 6.25

Combine like terms: 246 + 6.25 = 252.25
6.25 + 5x + x2 = 252.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 252.25

Calculate the square root of the right side: 15.882380174

Break this problem into two subproblems by setting 
(x + 2.5) equal to 15.882380174 and -15.882380174.


Subproblem 1
x + 2.5 = 15.882380174

Simplifying
x + 2.5 = 15.882380174

Reorder the terms:
2.5 + x = 15.882380174

Solving
2.5 + x = 15.882380174

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 = 15.882380174 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 15.882380174 + -2.5
x = 15.882380174 + -2.5

Combine like terms: 15.882380174 + -2.5 = 13.382380174
x = 13.382380174

Simplifying
x = 13.382380174


Subproblem 2
x + 2.5 = -15.882380174

Simplifying
x + 2.5 = -15.882380174

Reorder the terms:
2.5 + x = -15.882380174

Solving
2.5 + x = -15.882380174

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 = -15.882380174 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -15.882380174 + -2.5
x = -15.882380174 + -2.5

Combine like terms: -15.882380174 + -2.5 = -18.382380174
x = -18.382380174

Simplifying
x = -18.382380174


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {13.382380174, -18.382380174}

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