x^2+5x-275=0

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Solution for x^2+5x-275=0 equation: 


Simplifying
x2 + 5x + -275 = 0

Reorder the terms:
-275 + 5x + x2 = 0

Solving
-275 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '275' to each side of the equation.
-275 + 5x + 275 + x2 = 0 + 275

Reorder the terms:
-275 + 275 + 5x + x2 = 0 + 275

Combine like terms: -275 + 275 = 0
0 + 5x + x2 = 0 + 275
5x + x2 = 0 + 275

Combine like terms: 0 + 275 = 275
5x + x2 = 275

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 = 275 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 275 + 6.25

Combine like terms: 275 + 6.25 = 281.25
6.25 + 5x + x2 = 281.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 281.25

Calculate the square root of the right side: 16.770509831

Break this problem into two subproblems by setting 
(x + 2.5) equal to 16.770509831 and -16.770509831.


Subproblem 1
x + 2.5 = 16.770509831

Simplifying
x + 2.5 = 16.770509831

Reorder the terms:
2.5 + x = 16.770509831

Solving
2.5 + x = 16.770509831

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 = 16.770509831 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 16.770509831 + -2.5
x = 16.770509831 + -2.5

Combine like terms: 16.770509831 + -2.5 = 14.270509831
x = 14.270509831

Simplifying
x = 14.270509831


Subproblem 2
x + 2.5 = -16.770509831

Simplifying
x + 2.5 = -16.770509831

Reorder the terms:
2.5 + x = -16.770509831

Solving
2.5 + x = -16.770509831

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 = -16.770509831 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -16.770509831 + -2.5
x = -16.770509831 + -2.5

Combine like terms: -16.770509831 + -2.5 = -19.270509831
x = -19.270509831

Simplifying
x = -19.270509831


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {14.270509831, -19.270509831}

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