24x^2-336x+864=0

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Solution for 24x^2-336x+864=0 equation:


Simplifying
24x2 + -336x + 864 = 0

Reorder the terms:
864 + -336x + 24x2 = 0

Solving
864 + -336x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '24'.
24(36 + -14x + x2) = 0

Ignore the factor 24.

Subproblem 1
Set the factor '(36 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
36 + -14x + x2 = 0

Solving
36 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + -14x + -36 + x2 = 0 + -36

Reorder the terms:
36 + -36 + -14x + x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -14x + x2 = 0 + -36
-14x + x2 = 0 + -36

Combine like terms: 0 + -36 = -36
-14x + x2 = -36

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = -36 + 49

Reorder the terms:
49 + -14x + x2 = -36 + 49

Combine like terms: -36 + 49 = 13
49 + -14x + x2 = 13

Factor a perfect square on the left side:
(x + -7)(x + -7) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + -7) equal to 3.605551275 and -3.605551275.


Subproblem 1
x + -7 = 3.605551275

Simplifying
x + -7 = 3.605551275

Reorder the terms:
-7 + x = 3.605551275

Solving
-7 + x = 3.605551275

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 3.605551275 + 7

Combine like terms: -7 + 7 = 0
0 + x = 3.605551275 + 7
x = 3.605551275 + 7

Combine like terms: 3.605551275 + 7 = 10.605551275
x = 10.605551275

Simplifying
x = 10.605551275


Subproblem 2
x + -7 = -3.605551275

Simplifying
x + -7 = -3.605551275

Reorder the terms:
-7 + x = -3.605551275

Solving
-7 + x = -3.605551275

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -3.605551275 + 7

Combine like terms: -7 + 7 = 0
0 + x = -3.605551275 + 7
x = -3.605551275 + 7

Combine like terms: -3.605551275 + 7 = 3.394448725
x = 3.394448725

Simplifying
x = 3.394448725


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.605551275, 3.394448725}
Solution
x = {10.605551275, 3.394448725}

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