3x(x-4)+5=3x-2

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Solution for 3x(x-4)+5=3x-2 equation:


Simplifying
3x(x + -4) + 5 = 3x + -2

Reorder the terms:
3x(-4 + x) + 5 = 3x + -2
(-4 * 3x + x * 3x) + 5 = 3x + -2
(-12x + 3x2) + 5 = 3x + -2

Reorder the terms:
5 + -12x + 3x2 = 3x + -2

Reorder the terms:
5 + -12x + 3x2 = -2 + 3x

Solving
5 + -12x + 3x2 = -2 + 3x

Solving for variable 'x'.

Reorder the terms:
5 + 2 + -12x + -3x + 3x2 = -2 + 3x + 2 + -3x

Combine like terms: 5 + 2 = 7
7 + -12x + -3x + 3x2 = -2 + 3x + 2 + -3x

Combine like terms: -12x + -3x = -15x
7 + -15x + 3x2 = -2 + 3x + 2 + -3x

Reorder the terms:
7 + -15x + 3x2 = -2 + 2 + 3x + -3x

Combine like terms: -2 + 2 = 0
7 + -15x + 3x2 = 0 + 3x + -3x
7 + -15x + 3x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
7 + -15x + 3x2 = 0

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

Divide each side by '3'.
2.333333333 + -5x + x2 = 0

Move the constant term to the right:

Add '-2.333333333' to each side of the equation.
2.333333333 + -5x + -2.333333333 + x2 = 0 + -2.333333333

Reorder the terms:
2.333333333 + -2.333333333 + -5x + x2 = 0 + -2.333333333

Combine like terms: 2.333333333 + -2.333333333 = 0.000000000
0.000000000 + -5x + x2 = 0 + -2.333333333
-5x + x2 = 0 + -2.333333333

Combine like terms: 0 + -2.333333333 = -2.333333333
-5x + x2 = -2.333333333

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -2.333333333 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -2.333333333 + 6.25

Combine like terms: -2.333333333 + 6.25 = 3.916666667
6.25 + -5x + x2 = 3.916666667

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 3.916666667

Calculate the square root of the right side: 1.979057015

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.979057015 and -1.979057015.

Subproblem 1

x + -2.5 = 1.979057015 Simplifying x + -2.5 = 1.979057015 Reorder the terms: -2.5 + x = 1.979057015 Solving -2.5 + x = 1.979057015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.979057015 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.979057015 + 2.5 x = 1.979057015 + 2.5 Combine like terms: 1.979057015 + 2.5 = 4.479057015 x = 4.479057015 Simplifying x = 4.479057015

Subproblem 2

x + -2.5 = -1.979057015 Simplifying x + -2.5 = -1.979057015 Reorder the terms: -2.5 + x = -1.979057015 Solving -2.5 + x = -1.979057015 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.979057015 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.979057015 + 2.5 x = -1.979057015 + 2.5 Combine like terms: -1.979057015 + 2.5 = 0.520942985 x = 0.520942985 Simplifying x = 0.520942985

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.479057015, 0.520942985}

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