3x^2-24x-75=0

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Solution for 3x^2-24x-75=0 equation: 


Simplifying
3x2 + -24x + -75 = 0

Reorder the terms:
-75 + -24x + 3x2 = 0

Solving
-75 + -24x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-25 + -8x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-25 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
-25 + -8x + x2 = 0

Solving
-25 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -8x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + -8x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -8x + x2 = 0 + 25
-8x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-8x + x2 = 25

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = 25 + 16

Reorder the terms:
16 + -8x + x2 = 25 + 16

Combine like terms: 25 + 16 = 41
16 + -8x + x2 = 41

Factor a perfect square on the left side:
(x + -4)(x + -4) = 41

Calculate the square root of the right side: 6.403124237

Break this problem into two subproblems by setting 
(x + -4) equal to 6.403124237 and -6.403124237.


Subproblem 1
x + -4 = 6.403124237

Simplifying
x + -4 = 6.403124237

Reorder the terms:
-4 + x = 6.403124237

Solving
-4 + x = 6.403124237

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 6.403124237 + 4

Combine like terms: -4 + 4 = 0
0 + x = 6.403124237 + 4
x = 6.403124237 + 4

Combine like terms: 6.403124237 + 4 = 10.403124237
x = 10.403124237

Simplifying
x = 10.403124237


Subproblem 2
x + -4 = -6.403124237

Simplifying
x + -4 = -6.403124237

Reorder the terms:
-4 + x = -6.403124237

Solving
-4 + x = -6.403124237

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -6.403124237 + 4

Combine like terms: -4 + 4 = 0
0 + x = -6.403124237 + 4
x = -6.403124237 + 4

Combine like terms: -6.403124237 + 4 = -2.403124237
x = -2.403124237

Simplifying
x = -2.403124237


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.403124237, -2.403124237}
Solution
x = {10.403124237, -2.403124237}

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