3x^2-30x-75=-27

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Solution for 3x^2-30x-75=-27 equation: 


Simplifying
3x2 + -30x + -75 = -27

Reorder the terms:
-75 + -30x + 3x2 = -27

Solving
-75 + -30x + 3x2 = -27

Solving for variable 'x'.

Reorder the terms:
-75 + 27 + -30x + 3x2 = -27 + 27

Combine like terms: -75 + 27 = -48
-48 + -30x + 3x2 = -27 + 27

Combine like terms: -27 + 27 = 0
-48 + -30x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-16 + -10x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-16 + -10x + x2)' equal to zero and attempt to solve:

Simplifying
-16 + -10x + x2 = 0

Solving
-16 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '16' to each side of the equation.
-16 + -10x + 16 + x2 = 0 + 16

Reorder the terms:
-16 + 16 + -10x + x2 = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -10x + x2 = 0 + 16
-10x + x2 = 0 + 16

Combine like terms: 0 + 16 = 16
-10x + x2 = 16

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 16 + 25

Reorder the terms:
25 + -10x + x2 = 16 + 25

Combine like terms: 16 + 25 = 41
25 + -10x + x2 = 41

Factor a perfect square on the left side:
(x + -5)(x + -5) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x + -5) equal to 6.403124237 and -6.403124237.


Subproblem 1
x + -5 = 6.403124237

Simplifying
x + -5 = 6.403124237

Reorder the terms:
-5 + x = 6.403124237

Solving
-5 + x = 6.403124237

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 6.403124237 + 5

Combine like terms: -5 + 5 = 0
0 + x = 6.403124237 + 5
x = 6.403124237 + 5

Combine like terms: 6.403124237 + 5 = 11.403124237
x = 11.403124237

Simplifying
x = 11.403124237


Subproblem 2
x + -5 = -6.403124237

Simplifying
x + -5 = -6.403124237

Reorder the terms:
-5 + x = -6.403124237

Solving
-5 + x = -6.403124237

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -6.403124237 + 5

Combine like terms: -5 + 5 = 0
0 + x = -6.403124237 + 5
x = -6.403124237 + 5

Combine like terms: -6.403124237 + 5 = -1.403124237
x = -1.403124237

Simplifying
x = -1.403124237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.403124237, -1.403124237}
Solution
x = {11.403124237, -1.403124237}

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