x^2+5x-1440=0

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Solution for x^2+5x-1440=0 equation: 


Simplifying
x2 + 5x + -1440 = 0

Reorder the terms:
-1440 + 5x + x2 = 0

Solving
-1440 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1440' to each side of the equation.
-1440 + 5x + 1440 + x2 = 0 + 1440

Reorder the terms:
-1440 + 1440 + 5x + x2 = 0 + 1440

Combine like terms: -1440 + 1440 = 0
0 + 5x + x2 = 0 + 1440
5x + x2 = 0 + 1440

Combine like terms: 0 + 1440 = 1440
5x + x2 = 1440

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 = 1440 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 1440 + 6.25

Combine like terms: 1440 + 6.25 = 1446.25
6.25 + 5x + x2 = 1446.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 1446.25

Calculate the square root of the right side: 38.02959374

Break this problem into two subproblems by setting 
(x + 2.5) equal to 38.02959374 and -38.02959374.


Subproblem 1
x + 2.5 = 38.02959374

Simplifying
x + 2.5 = 38.02959374

Reorder the terms:
2.5 + x = 38.02959374

Solving
2.5 + x = 38.02959374

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 = 38.02959374 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 38.02959374 + -2.5
x = 38.02959374 + -2.5

Combine like terms: 38.02959374 + -2.5 = 35.52959374
x = 35.52959374

Simplifying
x = 35.52959374


Subproblem 2
x + 2.5 = -38.02959374

Simplifying
x + 2.5 = -38.02959374

Reorder the terms:
2.5 + x = -38.02959374

Solving
2.5 + x = -38.02959374

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 = -38.02959374 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -38.02959374 + -2.5
x = -38.02959374 + -2.5

Combine like terms: -38.02959374 + -2.5 = -40.52959374
x = -40.52959374

Simplifying
x = -40.52959374


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {35.52959374, -40.52959374}

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