x^2+6x-75=0

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Solution for x^2+6x-75=0 equation: 


Simplifying
x2 + 6x + -75 = 0

Reorder the terms:
-75 + 6x + x2 = 0

Solving
-75 + 6x + 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 + 6x + 75 + x2 = 0 + 75

Reorder the terms:
-75 + 75 + 6x + x2 = 0 + 75

Combine like terms: -75 + 75 = 0
0 + 6x + x2 = 0 + 75
6x + x2 = 0 + 75

Combine like terms: 0 + 75 = 75
6x + x2 = 75

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 75 + 9

Reorder the terms:
9 + 6x + x2 = 75 + 9

Combine like terms: 75 + 9 = 84
9 + 6x + x2 = 84

Factor a perfect square on the left side:
(x + 3)(x + 3) = 84

Calculate the square root of the right side: 9.16515139

Break this problem into two subproblems by setting 
(x + 3) equal to 9.16515139 and -9.16515139.


Subproblem 1
x + 3 = 9.16515139

Simplifying
x + 3 = 9.16515139

Reorder the terms:
3 + x = 9.16515139

Solving
3 + x = 9.16515139

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + x = 9.16515139 + -3

Combine like terms: 3 + -3 = 0
0 + x = 9.16515139 + -3
x = 9.16515139 + -3

Combine like terms: 9.16515139 + -3 = 6.16515139
x = 6.16515139

Simplifying
x = 6.16515139


Subproblem 2
x + 3 = -9.16515139

Simplifying
x + 3 = -9.16515139

Reorder the terms:
3 + x = -9.16515139

Solving
3 + x = -9.16515139

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + x = -9.16515139 + -3

Combine like terms: 3 + -3 = 0
0 + x = -9.16515139 + -3
x = -9.16515139 + -3

Combine like terms: -9.16515139 + -3 = -12.16515139
x = -12.16515139

Simplifying
x = -12.16515139


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.16515139, -12.16515139}

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