3x(4x+9)-4=34

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Solution for 3x(4x+9)-4=34 equation:


Simplifying
3x(4x + 9) + -4 = 34

Reorder the terms:
3x(9 + 4x) + -4 = 34
(9 * 3x + 4x * 3x) + -4 = 34
(27x + 12x2) + -4 = 34

Reorder the terms:
-4 + 27x + 12x2 = 34

Solving
-4 + 27x + 12x2 = 34

Solving for variable 'x'.

Reorder the terms:
-4 + -34 + 27x + 12x2 = 34 + -34

Combine like terms: -4 + -34 = -38
-38 + 27x + 12x2 = 34 + -34

Combine like terms: 34 + -34 = 0
-38 + 27x + 12x2 = 0

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

Divide each side by '12'.
-3.166666667 + 2.25x + x2 = 0

Move the constant term to the right:

Add '3.166666667' to each side of the equation.
-3.166666667 + 2.25x + 3.166666667 + x2 = 0 + 3.166666667

Reorder the terms:
-3.166666667 + 3.166666667 + 2.25x + x2 = 0 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + 2.25x + x2 = 0 + 3.166666667
2.25x + x2 = 0 + 3.166666667

Combine like terms: 0 + 3.166666667 = 3.166666667
2.25x + x2 = 3.166666667

The x term is 2.25x.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25x + 1.265625 + x2 = 3.166666667 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = 3.166666667 + 1.265625

Combine like terms: 3.166666667 + 1.265625 = 4.432291667
1.265625 + 2.25x + x2 = 4.432291667

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = 4.432291667

Calculate the square root of the right side: 2.10530085

Break this problem into two subproblems by setting 
(x + 1.125) equal to 2.10530085 and -2.10530085.


Subproblem 1
x + 1.125 = 2.10530085

Simplifying
x + 1.125 = 2.10530085

Reorder the terms:
1.125 + x = 2.10530085

Solving
1.125 + x = 2.10530085

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.125' to each side of the equation.
1.125 + -1.125 + x = 2.10530085 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = 2.10530085 + -1.125
x = 2.10530085 + -1.125

Combine like terms: 2.10530085 + -1.125 = 0.98030085
x = 0.98030085

Simplifying
x = 0.98030085


Subproblem 2
x + 1.125 = -2.10530085

Simplifying
x + 1.125 = -2.10530085

Reorder the terms:
1.125 + x = -2.10530085

Solving
1.125 + x = -2.10530085

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.125' to each side of the equation.
1.125 + -1.125 + x = -2.10530085 + -1.125

Combine like terms: 1.125 + -1.125 = 0.000
0.000 + x = -2.10530085 + -1.125
x = -2.10530085 + -1.125

Combine like terms: -2.10530085 + -1.125 = -3.23030085
x = -3.23030085

Simplifying
x = -3.23030085


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.98030085, -3.23030085}

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