(3x+4)(3x+4)=30

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Solution for (3x+4)(3x+4)=30 equation:


Simplifying
(3x + 4)(3x + 4) = 30

Reorder the terms:
(4 + 3x)(3x + 4) = 30

Reorder the terms:
(4 + 3x)(4 + 3x) = 30

Multiply (4 + 3x) * (4 + 3x)
(4(4 + 3x) + 3x * (4 + 3x)) = 30
((4 * 4 + 3x * 4) + 3x * (4 + 3x)) = 30
((16 + 12x) + 3x * (4 + 3x)) = 30
(16 + 12x + (4 * 3x + 3x * 3x)) = 30
(16 + 12x + (12x + 9x2)) = 30

Combine like terms: 12x + 12x = 24x
(16 + 24x + 9x2) = 30

Solving
16 + 24x + 9x2 = 30

Solving for variable 'x'.

Reorder the terms:
16 + -30 + 24x + 9x2 = 30 + -30

Combine like terms: 16 + -30 = -14
-14 + 24x + 9x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-14 + 24x + 9x2 = 0

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

Divide each side by '9'.
-1.555555556 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '1.555555556' to each side of the equation.
-1.555555556 + 2.666666667x + 1.555555556 + x2 = 0 + 1.555555556

Reorder the terms:
-1.555555556 + 1.555555556 + 2.666666667x + x2 = 0 + 1.555555556

Combine like terms: -1.555555556 + 1.555555556 = 0.000000000
0.000000000 + 2.666666667x + x2 = 0 + 1.555555556
2.666666667x + x2 = 0 + 1.555555556

Combine like terms: 0 + 1.555555556 = 1.555555556
2.666666667x + x2 = 1.555555556

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = 1.555555556 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = 1.555555556 + 1.777777780

Combine like terms: 1.555555556 + 1.777777780 = 3.333333336
1.777777780 + 2.666666667x + x2 = 3.333333336

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = 3.333333336

Calculate the square root of the right side: 1.825741859

Break this problem into two subproblems by setting 
(x + 1.333333334) equal to 1.825741859 and -1.825741859.

Subproblem 1

x + 1.333333334 = 1.825741859 Simplifying x + 1.333333334 = 1.825741859 Reorder the terms: 1.333333334 + x = 1.825741859 Solving 1.333333334 + x = 1.825741859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = 1.825741859 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = 1.825741859 + -1.333333334 x = 1.825741859 + -1.333333334 Combine like terms: 1.825741859 + -1.333333334 = 0.492408525 x = 0.492408525 Simplifying x = 0.492408525

Subproblem 2

x + 1.333333334 = -1.825741859 Simplifying x + 1.333333334 = -1.825741859 Reorder the terms: 1.333333334 + x = -1.825741859 Solving 1.333333334 + x = -1.825741859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.333333334' to each side of the equation. 1.333333334 + -1.333333334 + x = -1.825741859 + -1.333333334 Combine like terms: 1.333333334 + -1.333333334 = 0.000000000 0.000000000 + x = -1.825741859 + -1.333333334 x = -1.825741859 + -1.333333334 Combine like terms: -1.825741859 + -1.333333334 = -3.159075193 x = -3.159075193 Simplifying x = -3.159075193

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.492408525, -3.159075193}

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