3x(2x-4)=17

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Solution for 3x(2x-4)=17 equation:


Simplifying
3x(2x + -4) = 17

Reorder the terms:
3x(-4 + 2x) = 17
(-4 * 3x + 2x * 3x) = 17
(-12x + 6x2) = 17

Solving
-12x + 6x2 = 17

Solving for variable 'x'.

Reorder the terms:
-17 + -12x + 6x2 = 17 + -17

Combine like terms: 17 + -17 = 0
-17 + -12x + 6x2 = 0

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

Divide each side by '6'.
-2.833333333 + -2x + x2 = 0

Move the constant term to the right:

Add '2.833333333' to each side of the equation.
-2.833333333 + -2x + 2.833333333 + x2 = 0 + 2.833333333

Reorder the terms:
-2.833333333 + 2.833333333 + -2x + x2 = 0 + 2.833333333

Combine like terms: -2.833333333 + 2.833333333 = 0.000000000
0.000000000 + -2x + x2 = 0 + 2.833333333
-2x + x2 = 0 + 2.833333333

Combine like terms: 0 + 2.833333333 = 2.833333333
-2x + x2 = 2.833333333

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 2.833333333 + 1

Reorder the terms:
1 + -2x + x2 = 2.833333333 + 1

Combine like terms: 2.833333333 + 1 = 3.833333333
1 + -2x + x2 = 3.833333333

Factor a perfect square on the left side:
(x + -1)(x + -1) = 3.833333333

Calculate the square root of the right side: 1.957890021

Break this problem into two subproblems by setting 
(x + -1) equal to 1.957890021 and -1.957890021.

Subproblem 1

x + -1 = 1.957890021 Simplifying x + -1 = 1.957890021 Reorder the terms: -1 + x = 1.957890021 Solving -1 + x = 1.957890021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.957890021 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.957890021 + 1 x = 1.957890021 + 1 Combine like terms: 1.957890021 + 1 = 2.957890021 x = 2.957890021 Simplifying x = 2.957890021

Subproblem 2

x + -1 = -1.957890021 Simplifying x + -1 = -1.957890021 Reorder the terms: -1 + x = -1.957890021 Solving -1 + x = -1.957890021 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.957890021 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.957890021 + 1 x = -1.957890021 + 1 Combine like terms: -1.957890021 + 1 = -0.957890021 x = -0.957890021 Simplifying x = -0.957890021

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.957890021, -0.957890021}

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