x^2+5x-75=0

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Solution for x^2+5x-75=0 equation: 


Simplifying
x2 + 5x + -75 = 0

Reorder the terms:
-75 + 5x + x2 = 0

Solving
-75 + 5x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '75' to each side of the equation.
-75 + 5x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + 5x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + 5x + x2 = 0 + 75
5x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
5x + x2 = 75

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 = 75 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 75 + 6.25

Combine like terms: 75 + 6.25 = 81.25
6.25 + 5x + x2 = 81.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 81.25

Calculate the square root of the right side: 9.013878189

Break this problem into two subproblems by setting 
(x + 2.5) equal to 9.013878189 and -9.013878189.


Subproblem 1
x + 2.5 = 9.013878189

Simplifying
x + 2.5 = 9.013878189

Reorder the terms:
2.5 + x = 9.013878189

Solving
2.5 + x = 9.013878189

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 = 9.013878189 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 9.013878189 + -2.5
x = 9.013878189 + -2.5

Combine like terms: 9.013878189 + -2.5 = 6.513878189
x = 6.513878189

Simplifying
x = 6.513878189


Subproblem 2
x + 2.5 = -9.013878189

Simplifying
x + 2.5 = -9.013878189

Reorder the terms:
2.5 + x = -9.013878189

Solving
2.5 + x = -9.013878189

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 = -9.013878189 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -9.013878189 + -2.5
x = -9.013878189 + -2.5

Combine like terms: -9.013878189 + -2.5 = -11.513878189
x = -11.513878189

Simplifying
x = -11.513878189


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.513878189, -11.513878189}

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