(3x)(3x)-23x-8=0

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Solution for (3x)(3x)-23x-8=0 equation:


Simplifying
(3x)(3x) + -23x + -8 = 0

Remove parenthesis around (3x)
3x(3x) + -23x + -8 = 0

Remove parenthesis around (3x)
3x * 3x + -23x + -8 = 0

Reorder the terms for easier multiplication:
3 * 3x * x + -23x + -8 = 0

Multiply 3 * 3
9x * x + -23x + -8 = 0

Multiply x * x
9x2 + -23x + -8 = 0

Reorder the terms:
-8 + -23x + 9x2 = 0

Solving
-8 + -23x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-0.8888888889 + -2.555555556x + x2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + -2.555555556x + 0.8888888889 + x2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + -2.555555556x + x2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + -2.555555556x + x2 = 0 + 0.8888888889
-2.555555556x + x2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
-2.555555556x + x2 = 0.8888888889

The x term is -2.555555556x.  Take half its coefficient (-1.277777778).
Square it (1.632716050) and add it to both sides.

Add '1.632716050' to each side of the equation.
-2.555555556x + 1.632716050 + x2 = 0.8888888889 + 1.632716050

Reorder the terms:
1.632716050 + -2.555555556x + x2 = 0.8888888889 + 1.632716050

Combine like terms: 0.8888888889 + 1.632716050 = 2.5216049389
1.632716050 + -2.555555556x + x2 = 2.5216049389

Factor a perfect square on the left side:
(x + -1.277777778)(x + -1.277777778) = 2.5216049389

Calculate the square root of the right side: 1.587956214

Break this problem into two subproblems by setting 
(x + -1.277777778) equal to 1.587956214 and -1.587956214.

Subproblem 1

x + -1.277777778 = 1.587956214 Simplifying x + -1.277777778 = 1.587956214 Reorder the terms: -1.277777778 + x = 1.587956214 Solving -1.277777778 + x = 1.587956214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.277777778' to each side of the equation. -1.277777778 + 1.277777778 + x = 1.587956214 + 1.277777778 Combine like terms: -1.277777778 + 1.277777778 = 0.000000000 0.000000000 + x = 1.587956214 + 1.277777778 x = 1.587956214 + 1.277777778 Combine like terms: 1.587956214 + 1.277777778 = 2.865733992 x = 2.865733992 Simplifying x = 2.865733992

Subproblem 2

x + -1.277777778 = -1.587956214 Simplifying x + -1.277777778 = -1.587956214 Reorder the terms: -1.277777778 + x = -1.587956214 Solving -1.277777778 + x = -1.587956214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.277777778' to each side of the equation. -1.277777778 + 1.277777778 + x = -1.587956214 + 1.277777778 Combine like terms: -1.277777778 + 1.277777778 = 0.000000000 0.000000000 + x = -1.587956214 + 1.277777778 x = -1.587956214 + 1.277777778 Combine like terms: -1.587956214 + 1.277777778 = -0.310178436 x = -0.310178436 Simplifying x = -0.310178436

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.865733992, -0.310178436}

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