3x(3x)+8x-16=0

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Solution for 3x(3x)+8x-16=0 equation:


Simplifying
3x(3x) + 8x + -16 = 0

Remove parenthesis around (3x)
3x * 3x + 8x + -16 = 0

Reorder the terms for easier multiplication:
3 * 3x * x + 8x + -16 = 0

Multiply 3 * 3
9x * x + 8x + -16 = 0

Multiply x * x
9x2 + 8x + -16 = 0

Reorder the terms:
-16 + 8x + 9x2 = 0

Solving
-16 + 8x + 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'.
-1.777777778 + 0.8888888889x + x2 = 0

Move the constant term to the right:

Add '1.777777778' to each side of the equation.
-1.777777778 + 0.8888888889x + 1.777777778 + x2 = 0 + 1.777777778

Reorder the terms:
-1.777777778 + 1.777777778 + 0.8888888889x + x2 = 0 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + 0.8888888889x + x2 = 0 + 1.777777778
0.8888888889x + x2 = 0 + 1.777777778

Combine like terms: 0 + 1.777777778 = 1.777777778
0.8888888889x + x2 = 1.777777778

The x term is 0.8888888889x.  Take half its coefficient (0.4444444445).
Square it (0.1975308642) and add it to both sides.

Add '0.1975308642' to each side of the equation.
0.8888888889x + 0.1975308642 + x2 = 1.777777778 + 0.1975308642

Reorder the terms:
0.1975308642 + 0.8888888889x + x2 = 1.777777778 + 0.1975308642

Combine like terms: 1.777777778 + 0.1975308642 = 1.9753086422
0.1975308642 + 0.8888888889x + x2 = 1.9753086422

Factor a perfect square on the left side:
(x + 0.4444444445)(x + 0.4444444445) = 1.9753086422

Calculate the square root of the right side: 1.405456738

Break this problem into two subproblems by setting 
(x + 0.4444444445) equal to 1.405456738 and -1.405456738.

Subproblem 1

x + 0.4444444445 = 1.405456738 Simplifying x + 0.4444444445 = 1.405456738 Reorder the terms: 0.4444444445 + x = 1.405456738 Solving 0.4444444445 + x = 1.405456738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = 1.405456738 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = 1.405456738 + -0.4444444445 x = 1.405456738 + -0.4444444445 Combine like terms: 1.405456738 + -0.4444444445 = 0.9610122935 x = 0.9610122935 Simplifying x = 0.9610122935

Subproblem 2

x + 0.4444444445 = -1.405456738 Simplifying x + 0.4444444445 = -1.405456738 Reorder the terms: 0.4444444445 + x = -1.405456738 Solving 0.4444444445 + x = -1.405456738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = -1.405456738 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = -1.405456738 + -0.4444444445 x = -1.405456738 + -0.4444444445 Combine like terms: -1.405456738 + -0.4444444445 = -1.8499011825 x = -1.8499011825 Simplifying x = -1.8499011825

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.9610122935, -1.8499011825}

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