(2x-4)-15x(x-5)=

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Solution for (2x-4)-15x(x-5)= equation:


Simplifying
(2x + -4) + -15x(x + -5) = 0

Reorder the terms:
(-4 + 2x) + -15x(x + -5) = 0

Remove parenthesis around (-4 + 2x)
-4 + 2x + -15x(x + -5) = 0

Reorder the terms:
-4 + 2x + -15x(-5 + x) = 0
-4 + 2x + (-5 * -15x + x * -15x) = 0
-4 + 2x + (75x + -15x2) = 0

Combine like terms: 2x + 75x = 77x
-4 + 77x + -15x2 = 0

Solving
-4 + 77x + -15x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-15 the coefficient of the squared term: 

Divide each side by '-15'.
0.2666666667 + -5.133333333x + x2 = 0

Move the constant term to the right:

Add '-0.2666666667' to each side of the equation.
0.2666666667 + -5.133333333x + -0.2666666667 + x2 = 0 + -0.2666666667

Reorder the terms:
0.2666666667 + -0.2666666667 + -5.133333333x + x2 = 0 + -0.2666666667

Combine like terms: 0.2666666667 + -0.2666666667 = 0.0000000000
0.0000000000 + -5.133333333x + x2 = 0 + -0.2666666667
-5.133333333x + x2 = 0 + -0.2666666667

Combine like terms: 0 + -0.2666666667 = -0.2666666667
-5.133333333x + x2 = -0.2666666667

The x term is -5.133333333x.  Take half its coefficient (-2.566666667).
Square it (6.587777779) and add it to both sides.

Add '6.587777779' to each side of the equation.
-5.133333333x + 6.587777779 + x2 = -0.2666666667 + 6.587777779

Reorder the terms:
6.587777779 + -5.133333333x + x2 = -0.2666666667 + 6.587777779

Combine like terms: -0.2666666667 + 6.587777779 = 6.3211111123
6.587777779 + -5.133333333x + x2 = 6.3211111123

Factor a perfect square on the left side:
(x + -2.566666667)(x + -2.566666667) = 6.3211111123

Calculate the square root of the right side: 2.514181997

Break this problem into two subproblems by setting 
(x + -2.566666667) equal to 2.514181997 and -2.514181997.

Subproblem 1

x + -2.566666667 = 2.514181997 Simplifying x + -2.566666667 = 2.514181997 Reorder the terms: -2.566666667 + x = 2.514181997 Solving -2.566666667 + x = 2.514181997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.566666667' to each side of the equation. -2.566666667 + 2.566666667 + x = 2.514181997 + 2.566666667 Combine like terms: -2.566666667 + 2.566666667 = 0.000000000 0.000000000 + x = 2.514181997 + 2.566666667 x = 2.514181997 + 2.566666667 Combine like terms: 2.514181997 + 2.566666667 = 5.080848664 x = 5.080848664 Simplifying x = 5.080848664

Subproblem 2

x + -2.566666667 = -2.514181997 Simplifying x + -2.566666667 = -2.514181997 Reorder the terms: -2.566666667 + x = -2.514181997 Solving -2.566666667 + x = -2.514181997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.566666667' to each side of the equation. -2.566666667 + 2.566666667 + x = -2.514181997 + 2.566666667 Combine like terms: -2.566666667 + 2.566666667 = 0.000000000 0.000000000 + x = -2.514181997 + 2.566666667 x = -2.514181997 + 2.566666667 Combine like terms: -2.514181997 + 2.566666667 = 0.05248467 x = 0.05248467 Simplifying x = 0.05248467

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.080848664, 0.05248467}

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