3x^2-24x-15=0

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Solution for 3x^2-24x-15=0 equation:


Simplifying
3x2 + -24x + -15 = 0

Reorder the terms:
-15 + -24x + 3x2 = 0

Solving
-15 + -24x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -8x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-5 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
-5 + -8x + x2 = 0

Solving
-5 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -8x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + -8x + x2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -8x + x2 = 0 + 5
-8x + x2 = 0 + 5

Combine like terms: 0 + 5 = 5
-8x + x2 = 5

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 = 5 + 16

Reorder the terms:
16 + -8x + x2 = 5 + 16

Combine like terms: 5 + 16 = 21
16 + -8x + x2 = 21

Factor a perfect square on the left side:
(x + -4)(x + -4) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(x + -4) equal to 4.582575695 and -4.582575695.


Subproblem 1
x + -4 = 4.582575695

Simplifying
x + -4 = 4.582575695

Reorder the terms:
-4 + x = 4.582575695

Solving
-4 + x = 4.582575695

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 = 4.582575695 + 4

Combine like terms: -4 + 4 = 0
0 + x = 4.582575695 + 4
x = 4.582575695 + 4

Combine like terms: 4.582575695 + 4 = 8.582575695
x = 8.582575695

Simplifying
x = 8.582575695


Subproblem 2
x + -4 = -4.582575695

Simplifying
x + -4 = -4.582575695

Reorder the terms:
-4 + x = -4.582575695

Solving
-4 + x = -4.582575695

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 = -4.582575695 + 4

Combine like terms: -4 + 4 = 0
0 + x = -4.582575695 + 4
x = -4.582575695 + 4

Combine like terms: -4.582575695 + 4 = -0.582575695
x = -0.582575695

Simplifying
x = -0.582575695


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.582575695, -0.582575695}
Solution
x = {8.582575695, -0.582575695}

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