3x^2-24x-45=0

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Solution for 3x^2-24x-45=0 equation: 


Simplifying
3x2 + -24x + -45 = 0

Reorder the terms:
-45 + -24x + 3x2 = 0

Solving
-45 + -24x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -8x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-15 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
-15 + -8x + x2 = 0

Solving
-15 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -8x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -8x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -8x + x2 = 0 + 15
-8x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-8x + x2 = 15

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 = 15 + 16

Reorder the terms:
16 + -8x + x2 = 15 + 16

Combine like terms: 15 + 16 = 31
16 + -8x + x2 = 31

Factor a perfect square on the left side:
(x + -4)(x + -4) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(x + -4) equal to 5.567764363 and -5.567764363.


Subproblem 1
x + -4 = 5.567764363

Simplifying
x + -4 = 5.567764363

Reorder the terms:
-4 + x = 5.567764363

Solving
-4 + x = 5.567764363

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 = 5.567764363 + 4

Combine like terms: -4 + 4 = 0
0 + x = 5.567764363 + 4
x = 5.567764363 + 4

Combine like terms: 5.567764363 + 4 = 9.567764363
x = 9.567764363

Simplifying
x = 9.567764363


Subproblem 2
x + -4 = -5.567764363

Simplifying
x + -4 = -5.567764363

Reorder the terms:
-4 + x = -5.567764363

Solving
-4 + x = -5.567764363

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 = -5.567764363 + 4

Combine like terms: -4 + 4 = 0
0 + x = -5.567764363 + 4
x = -5.567764363 + 4

Combine like terms: -5.567764363 + 4 = -1.567764363
x = -1.567764363

Simplifying
x = -1.567764363


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.567764363, -1.567764363}
Solution
x = {9.567764363, -1.567764363}

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