(5x-2)(2x)=115

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Solution for (5x-2)(2x)=115 equation:


Simplifying
(5x + -2)(2x) = 115

Reorder the terms:
(-2 + 5x)(2x) = 115

Remove parenthesis around (2x)
(-2 + 5x) * 2x = 115

Reorder the terms for easier multiplication:
2x(-2 + 5x) = 115
(-2 * 2x + 5x * 2x) = 115
(-4x + 10x2) = 115

Solving
-4x + 10x2 = 115

Solving for variable 'x'.

Reorder the terms:
-115 + -4x + 10x2 = 115 + -115

Combine like terms: 115 + -115 = 0
-115 + -4x + 10x2 = 0

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

Divide each side by '10'.
-11.5 + -0.4x + x2 = 0.0

Move the constant term to the right:

Add '11.5' to each side of the equation.
-11.5 + -0.4x + 11.5 + x2 = 0.0 + 11.5

Reorder the terms:
-11.5 + 11.5 + -0.4x + x2 = 0.0 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + -0.4x + x2 = 0.0 + 11.5
-0.4x + x2 = 0.0 + 11.5

Combine like terms: 0.0 + 11.5 = 11.5
-0.4x + x2 = 11.5

The x term is -0.4x.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4x + 0.04 + x2 = 11.5 + 0.04

Reorder the terms:
0.04 + -0.4x + x2 = 11.5 + 0.04

Combine like terms: 11.5 + 0.04 = 11.54
0.04 + -0.4x + x2 = 11.54

Factor a perfect square on the left side:
(x + -0.2)(x + -0.2) = 11.54

Calculate the square root of the right side: 3.39705755

Break this problem into two subproblems by setting 
(x + -0.2) equal to 3.39705755 and -3.39705755.

Subproblem 1

x + -0.2 = 3.39705755 Simplifying x + -0.2 = 3.39705755 Reorder the terms: -0.2 + x = 3.39705755 Solving -0.2 + x = 3.39705755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 3.39705755 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 3.39705755 + 0.2 x = 3.39705755 + 0.2 Combine like terms: 3.39705755 + 0.2 = 3.59705755 x = 3.59705755 Simplifying x = 3.59705755

Subproblem 2

x + -0.2 = -3.39705755 Simplifying x + -0.2 = -3.39705755 Reorder the terms: -0.2 + x = -3.39705755 Solving -0.2 + x = -3.39705755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -3.39705755 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -3.39705755 + 0.2 x = -3.39705755 + 0.2 Combine like terms: -3.39705755 + 0.2 = -3.19705755 x = -3.19705755 Simplifying x = -3.19705755

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.59705755, -3.19705755}

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