(3x)(3x)+2x-16=0

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Solution for (3x)(3x)+2x-16=0 equation:


Simplifying
(3x)(3x) + 2x + -16 = 0

Remove parenthesis around (3x)
3x(3x) + 2x + -16 = 0

Remove parenthesis around (3x)
3x * 3x + 2x + -16 = 0

Reorder the terms for easier multiplication:
3 * 3x * x + 2x + -16 = 0

Multiply 3 * 3
9x * x + 2x + -16 = 0

Multiply x * x
9x2 + 2x + -16 = 0

Reorder the terms:
-16 + 2x + 9x2 = 0

Solving
-16 + 2x + 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 + 0.2222222222x + x2 = 0

Move the constant term to the right:

Add '1.777777778' to each side of the equation.
-1.777777778 + 0.2222222222x + 1.777777778 + x2 = 0 + 1.777777778

Reorder the terms:
-1.777777778 + 1.777777778 + 0.2222222222x + x2 = 0 + 1.777777778

Combine like terms: -1.777777778 + 1.777777778 = 0.000000000
0.000000000 + 0.2222222222x + x2 = 0 + 1.777777778
0.2222222222x + x2 = 0 + 1.777777778

Combine like terms: 0 + 1.777777778 = 1.777777778
0.2222222222x + x2 = 1.777777778

The x term is 0.2222222222x.  Take half its coefficient (0.1111111111).
Square it (0.01234567901) and add it to both sides.

Add '0.01234567901' to each side of the equation.
0.2222222222x + 0.01234567901 + x2 = 1.777777778 + 0.01234567901

Reorder the terms:
0.01234567901 + 0.2222222222x + x2 = 1.777777778 + 0.01234567901

Combine like terms: 1.777777778 + 0.01234567901 = 1.79012345701
0.01234567901 + 0.2222222222x + x2 = 1.79012345701

Factor a perfect square on the left side:
(x + 0.1111111111)(x + 0.1111111111) = 1.79012345701

Calculate the square root of the right side: 1.337954953

Break this problem into two subproblems by setting 
(x + 0.1111111111) equal to 1.337954953 and -1.337954953.

Subproblem 1

x + 0.1111111111 = 1.337954953 Simplifying x + 0.1111111111 = 1.337954953 Reorder the terms: 0.1111111111 + x = 1.337954953 Solving 0.1111111111 + x = 1.337954953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = 1.337954953 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = 1.337954953 + -0.1111111111 x = 1.337954953 + -0.1111111111 Combine like terms: 1.337954953 + -0.1111111111 = 1.2268438419 x = 1.2268438419 Simplifying x = 1.2268438419

Subproblem 2

x + 0.1111111111 = -1.337954953 Simplifying x + 0.1111111111 = -1.337954953 Reorder the terms: 0.1111111111 + x = -1.337954953 Solving 0.1111111111 + x = -1.337954953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1111111111' to each side of the equation. 0.1111111111 + -0.1111111111 + x = -1.337954953 + -0.1111111111 Combine like terms: 0.1111111111 + -0.1111111111 = 0.0000000000 0.0000000000 + x = -1.337954953 + -0.1111111111 x = -1.337954953 + -0.1111111111 Combine like terms: -1.337954953 + -0.1111111111 = -1.4490660641 x = -1.4490660641 Simplifying x = -1.4490660641

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.2268438419, -1.4490660641}

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