(3x+2)*(3x+2)-8=7

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Solution for (3x+2)*(3x+2)-8=7 equation:


Simplifying
(3x + 2)(3x + 2) + -8 = 7

Reorder the terms:
(2 + 3x)(3x + 2) + -8 = 7

Reorder the terms:
(2 + 3x)(2 + 3x) + -8 = 7

Multiply (2 + 3x) * (2 + 3x)
(2(2 + 3x) + 3x * (2 + 3x)) + -8 = 7
((2 * 2 + 3x * 2) + 3x * (2 + 3x)) + -8 = 7
((4 + 6x) + 3x * (2 + 3x)) + -8 = 7
(4 + 6x + (2 * 3x + 3x * 3x)) + -8 = 7
(4 + 6x + (6x + 9x2)) + -8 = 7

Combine like terms: 6x + 6x = 12x
(4 + 12x + 9x2) + -8 = 7

Reorder the terms:
4 + -8 + 12x + 9x2 = 7

Combine like terms: 4 + -8 = -4
-4 + 12x + 9x2 = 7

Solving
-4 + 12x + 9x2 = 7

Solving for variable 'x'.

Reorder the terms:
-4 + -7 + 12x + 9x2 = 7 + -7

Combine like terms: -4 + -7 = -11
-11 + 12x + 9x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-11 + 12x + 9x2 = 0

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

Divide each side by '9'.
-1.222222222 + 1.333333333x + x2 = 0

Move the constant term to the right:

Add '1.222222222' to each side of the equation.
-1.222222222 + 1.333333333x + 1.222222222 + x2 = 0 + 1.222222222

Reorder the terms:
-1.222222222 + 1.222222222 + 1.333333333x + x2 = 0 + 1.222222222

Combine like terms: -1.222222222 + 1.222222222 = 0.000000000
0.000000000 + 1.333333333x + x2 = 0 + 1.222222222
1.333333333x + x2 = 0 + 1.222222222

Combine like terms: 0 + 1.222222222 = 1.222222222
1.333333333x + x2 = 1.222222222

The x term is 1.333333333x.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333x + 0.4444444442 + x2 = 1.222222222 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333x + x2 = 1.222222222 + 0.4444444442

Combine like terms: 1.222222222 + 0.4444444442 = 1.6666666662
0.4444444442 + 1.333333333x + x2 = 1.6666666662

Factor a perfect square on the left side:
(x + 0.6666666665)(x + 0.6666666665) = 1.6666666662

Calculate the square root of the right side: 1.290994449

Break this problem into two subproblems by setting 
(x + 0.6666666665) equal to 1.290994449 and -1.290994449.

Subproblem 1

x + 0.6666666665 = 1.290994449 Simplifying x + 0.6666666665 = 1.290994449 Reorder the terms: 0.6666666665 + x = 1.290994449 Solving 0.6666666665 + x = 1.290994449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = 1.290994449 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 1.290994449 + -0.6666666665 x = 1.290994449 + -0.6666666665 Combine like terms: 1.290994449 + -0.6666666665 = 0.6243277825 x = 0.6243277825 Simplifying x = 0.6243277825

Subproblem 2

x + 0.6666666665 = -1.290994449 Simplifying x + 0.6666666665 = -1.290994449 Reorder the terms: 0.6666666665 + x = -1.290994449 Solving 0.6666666665 + x = -1.290994449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6666666665' to each side of the equation. 0.6666666665 + -0.6666666665 + x = -1.290994449 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -1.290994449 + -0.6666666665 x = -1.290994449 + -0.6666666665 Combine like terms: -1.290994449 + -0.6666666665 = -1.9576611155 x = -1.9576611155 Simplifying x = -1.9576611155

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.6243277825, -1.9576611155}

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