x(3x-14)=96

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Solution for x(3x-14)=96 equation: 


Simplifying
x(3x + -14) = 96

Reorder the terms:
x(-14 + 3x) = 96
(-14 * x + 3x * x) = 96
(-14x + 3x2) = 96

Solving
-14x + 3x2 = 96

Solving for variable 'x'.

Reorder the terms:
-96 + -14x + 3x2 = 96 + -96

Combine like terms: 96 + -96 = 0
-96 + -14x + 3x2 = 0

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

Divide each side by '3'.
-32 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '32' to each side of the equation.
-32 + -4.666666667x + 32 + x2 = 0 + 32

Reorder the terms:
-32 + 32 + -4.666666667x + x2 = 0 + 32

Combine like terms: -32 + 32 = 0
0 + -4.666666667x + x2 = 0 + 32
-4.666666667x + x2 = 0 + 32

Combine like terms: 0 + 32 = 32
-4.666666667x + x2 = 32

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = 32 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 32 + 5.444444448

Combine like terms: 32 + 5.444444448 = 37.444444448
5.444444448 + -4.666666667x + x2 = 37.444444448

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 37.444444448

Calculate the square root of the right side: 6.119186584

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 6.119186584 and -6.119186584.


Subproblem 1
x + -2.333333334 = 6.119186584

Simplifying
x + -2.333333334 = 6.119186584

Reorder the terms:
-2.333333334 + x = 6.119186584

Solving
-2.333333334 + x = 6.119186584

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = 6.119186584 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 6.119186584 + 2.333333334
x = 6.119186584 + 2.333333334

Combine like terms: 6.119186584 + 2.333333334 = 8.452519918
x = 8.452519918

Simplifying
x = 8.452519918


Subproblem 2
x + -2.333333334 = -6.119186584

Simplifying
x + -2.333333334 = -6.119186584

Reorder the terms:
-2.333333334 + x = -6.119186584

Solving
-2.333333334 + x = -6.119186584

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = -6.119186584 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -6.119186584 + 2.333333334
x = -6.119186584 + 2.333333334

Combine like terms: -6.119186584 + 2.333333334 = -3.78585325
x = -3.78585325

Simplifying
x = -3.78585325


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.452519918, -3.78585325}

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