3x^2-16x=336

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Solution for 3x^2-16x=336 equation:


Simplifying
3x2 + -16x = 336

Reorder the terms:
-16x + 3x2 = 336

Solving
-16x + 3x2 = 336

Solving for variable 'x'.

Reorder the terms:
-336 + -16x + 3x2 = 336 + -336

Combine like terms: 336 + -336 = 0
-336 + -16x + 3x2 = 0

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

Divide each side by '3'.
-112 + -5.333333333x + x2 = 0

Move the constant term to the right:

Add '112' to each side of the equation.
-112 + -5.333333333x + 112 + x2 = 0 + 112

Reorder the terms:
-112 + 112 + -5.333333333x + x2 = 0 + 112

Combine like terms: -112 + 112 = 0
0 + -5.333333333x + x2 = 0 + 112
-5.333333333x + x2 = 0 + 112

Combine like terms: 0 + 112 = 112
-5.333333333x + x2 = 112

The x term is -5.333333333x.  Take half its coefficient (-2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
-5.333333333x + 7.111111113 + x2 = 112 + 7.111111113

Reorder the terms:
7.111111113 + -5.333333333x + x2 = 112 + 7.111111113

Combine like terms: 112 + 7.111111113 = 119.111111113
7.111111113 + -5.333333333x + x2 = 119.111111113

Factor a perfect square on the left side:
(x + -2.666666667)(x + -2.666666667) = 119.111111113

Calculate the square root of the right side: 10.913803696

Break this problem into two subproblems by setting 
(x + -2.666666667) equal to 10.913803696 and -10.913803696.

Subproblem 1

x + -2.666666667 = 10.913803696 Simplifying x + -2.666666667 = 10.913803696 Reorder the terms: -2.666666667 + x = 10.913803696 Solving -2.666666667 + x = 10.913803696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + x = 10.913803696 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = 10.913803696 + 2.666666667 x = 10.913803696 + 2.666666667 Combine like terms: 10.913803696 + 2.666666667 = 13.580470363 x = 13.580470363 Simplifying x = 13.580470363

Subproblem 2

x + -2.666666667 = -10.913803696 Simplifying x + -2.666666667 = -10.913803696 Reorder the terms: -2.666666667 + x = -10.913803696 Solving -2.666666667 + x = -10.913803696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.666666667' to each side of the equation. -2.666666667 + 2.666666667 + x = -10.913803696 + 2.666666667 Combine like terms: -2.666666667 + 2.666666667 = 0.000000000 0.000000000 + x = -10.913803696 + 2.666666667 x = -10.913803696 + 2.666666667 Combine like terms: -10.913803696 + 2.666666667 = -8.247137029 x = -8.247137029 Simplifying x = -8.247137029

Solution

The solution to the problem is based on the solutions from the subproblems. x = {13.580470363, -8.247137029}

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