x^2+5x-140=0

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Solution for x^2+5x-140=0 equation: 


Simplifying
x2 + 5x + -140 = 0

Reorder the terms:
-140 + 5x + x2 = 0

Solving
-140 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '140' to each side of the equation.
-140 + 5x + 140 + x2 = 0 + 140

Reorder the terms:
-140 + 140 + 5x + x2 = 0 + 140

Combine like terms: -140 + 140 = 0
0 + 5x + x2 = 0 + 140
5x + x2 = 0 + 140

Combine like terms: 0 + 140 = 140
5x + x2 = 140

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 = 140 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 140 + 6.25

Combine like terms: 140 + 6.25 = 146.25
6.25 + 5x + x2 = 146.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 146.25

Calculate the square root of the right side: 12.093386622

Break this problem into two subproblems by setting 
(x + 2.5) equal to 12.093386622 and -12.093386622.


Subproblem 1
x + 2.5 = 12.093386622

Simplifying
x + 2.5 = 12.093386622

Reorder the terms:
2.5 + x = 12.093386622

Solving
2.5 + x = 12.093386622

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 = 12.093386622 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 12.093386622 + -2.5
x = 12.093386622 + -2.5

Combine like terms: 12.093386622 + -2.5 = 9.593386622
x = 9.593386622

Simplifying
x = 9.593386622


Subproblem 2
x + 2.5 = -12.093386622

Simplifying
x + 2.5 = -12.093386622

Reorder the terms:
2.5 + x = -12.093386622

Solving
2.5 + x = -12.093386622

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 = -12.093386622 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -12.093386622 + -2.5
x = -12.093386622 + -2.5

Combine like terms: -12.093386622 + -2.5 = -14.593386622
x = -14.593386622

Simplifying
x = -14.593386622


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.593386622, -14.593386622}

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