3x(8x+3)=63

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Solution for 3x(8x+3)=63 equation:


Simplifying
3x(8x + 3) = 63

Reorder the terms:
3x(3 + 8x) = 63
(3 * 3x + 8x * 3x) = 63
(9x + 24x2) = 63

Solving
9x + 24x2 = 63

Solving for variable 'x'.

Reorder the terms:
-63 + 9x + 24x2 = 63 + -63

Combine like terms: 63 + -63 = 0
-63 + 9x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-21 + 3x + 8x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-21 + 3x + 8x2)' equal to zero and attempt to solve:

Simplifying
-21 + 3x + 8x2 = 0

Solving
-21 + 3x + 8x2 = 0

Begin completing the square.  Divide all terms by
8 the coefficient of the squared term: 

Divide each side by '8'.
-2.625 + 0.375x + x2 = 0

Move the constant term to the right:

Add '2.625' to each side of the equation.
-2.625 + 0.375x + 2.625 + x2 = 0 + 2.625

Reorder the terms:
-2.625 + 2.625 + 0.375x + x2 = 0 + 2.625

Combine like terms: -2.625 + 2.625 = 0.000
0.000 + 0.375x + x2 = 0 + 2.625
0.375x + x2 = 0 + 2.625

Combine like terms: 0 + 2.625 = 2.625
0.375x + x2 = 2.625

The x term is 0.375x.  Take half its coefficient (0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
0.375x + 0.03515625 + x2 = 2.625 + 0.03515625

Reorder the terms:
0.03515625 + 0.375x + x2 = 2.625 + 0.03515625

Combine like terms: 2.625 + 0.03515625 = 2.66015625
0.03515625 + 0.375x + x2 = 2.66015625

Factor a perfect square on the left side:
(x + 0.1875)(x + 0.1875) = 2.66015625

Calculate the square root of the right side: 1.630998544

Break this problem into two subproblems by setting 
(x + 0.1875) equal to 1.630998544 and -1.630998544.


Subproblem 1
x + 0.1875 = 1.630998544

Simplifying
x + 0.1875 = 1.630998544

Reorder the terms:
0.1875 + x = 1.630998544

Solving
0.1875 + x = 1.630998544

Solving for variable 'x'.

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

Add '-0.1875' to each side of the equation.
0.1875 + -0.1875 + x = 1.630998544 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + x = 1.630998544 + -0.1875
x = 1.630998544 + -0.1875

Combine like terms: 1.630998544 + -0.1875 = 1.443498544
x = 1.443498544

Simplifying
x = 1.443498544


Subproblem 2
x + 0.1875 = -1.630998544

Simplifying
x + 0.1875 = -1.630998544

Reorder the terms:
0.1875 + x = -1.630998544

Solving
0.1875 + x = -1.630998544

Solving for variable 'x'.

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

Add '-0.1875' to each side of the equation.
0.1875 + -0.1875 + x = -1.630998544 + -0.1875

Combine like terms: 0.1875 + -0.1875 = 0.0000
0.0000 + x = -1.630998544 + -0.1875
x = -1.630998544 + -0.1875

Combine like terms: -1.630998544 + -0.1875 = -1.818498544
x = -1.818498544

Simplifying
x = -1.818498544


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.443498544, -1.818498544}
Solution
x = {1.443498544, -1.818498544}

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