2x+3x(x-5)=130

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Solution for 2x+3x(x-5)=130 equation:


Simplifying
2x + 3x(x + -5) = 130

Reorder the terms:
2x + 3x(-5 + x) = 130
2x + (-5 * 3x + x * 3x) = 130
2x + (-15x + 3x2) = 130

Combine like terms: 2x + -15x = -13x
-13x + 3x2 = 130

Solving
-13x + 3x2 = 130

Solving for variable 'x'.

Reorder the terms:
-130 + -13x + 3x2 = 130 + -130

Combine like terms: 130 + -130 = 0
-130 + -13x + 3x2 = 0

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

Divide each side by '3'.
-43.33333333 + -4.333333333x + x2 = 0

Move the constant term to the right:

Add '43.33333333' to each side of the equation.
-43.33333333 + -4.333333333x + 43.33333333 + x2 = 0 + 43.33333333

Reorder the terms:
-43.33333333 + 43.33333333 + -4.333333333x + x2 = 0 + 43.33333333

Combine like terms: -43.33333333 + 43.33333333 = 0.00000000
0.00000000 + -4.333333333x + x2 = 0 + 43.33333333
-4.333333333x + x2 = 0 + 43.33333333

Combine like terms: 0 + 43.33333333 = 43.33333333
-4.333333333x + x2 = 43.33333333

The x term is -4.333333333x.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333x + 4.694444446 + x2 = 43.33333333 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333x + x2 = 43.33333333 + 4.694444446

Combine like terms: 43.33333333 + 4.694444446 = 48.027777776
4.694444446 + -4.333333333x + x2 = 48.027777776

Factor a perfect square on the left side:
(x + -2.166666667)(x + -2.166666667) = 48.027777776

Calculate the square root of the right side: 6.930207629

Break this problem into two subproblems by setting 
(x + -2.166666667) equal to 6.930207629 and -6.930207629.

Subproblem 1

x + -2.166666667 = 6.930207629 Simplifying x + -2.166666667 = 6.930207629 Reorder the terms: -2.166666667 + x = 6.930207629 Solving -2.166666667 + x = 6.930207629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = 6.930207629 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = 6.930207629 + 2.166666667 x = 6.930207629 + 2.166666667 Combine like terms: 6.930207629 + 2.166666667 = 9.096874296 x = 9.096874296 Simplifying x = 9.096874296

Subproblem 2

x + -2.166666667 = -6.930207629 Simplifying x + -2.166666667 = -6.930207629 Reorder the terms: -2.166666667 + x = -6.930207629 Solving -2.166666667 + x = -6.930207629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.166666667' to each side of the equation. -2.166666667 + 2.166666667 + x = -6.930207629 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + x = -6.930207629 + 2.166666667 x = -6.930207629 + 2.166666667 Combine like terms: -6.930207629 + 2.166666667 = -4.763540962 x = -4.763540962 Simplifying x = -4.763540962

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.096874296, -4.763540962}

 

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