0.5(x-5)(x-15)=0

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Solution for 0.5(x-5)(x-15)=0 equation:


Simplifying
0.5(x + -5)(x + -15) = 0

Reorder the terms:
0.5(-5 + x)(x + -15) = 0

Reorder the terms:
0.5(-5 + x)(-15 + x) = 0

Multiply (-5 + x) * (-15 + x)
0.5(-5(-15 + x) + x(-15 + x)) = 0
0.5((-15 * -5 + x * -5) + x(-15 + x)) = 0
0.5((75 + -5x) + x(-15 + x)) = 0
0.5(75 + -5x + (-15 * x + x * x)) = 0
0.5(75 + -5x + (-15x + x2)) = 0

Combine like terms: -5x + -15x = -20x
0.5(75 + -20x + x2) = 0
(75 * 0.5 + -20x * 0.5 + x2 * 0.5) = 0
(37.5 + -10x + 0.5x2) = 0

Solving
37.5 + -10x + 0.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.5'.
75 + -20x + x2 = 0

Move the constant term to the right:

Add '-75' to each side of the equation.
75 + -20x + -75 + x2 = 0 + -75

Reorder the terms:
75 + -75 + -20x + x2 = 0 + -75

Combine like terms: 75 + -75 = 0
0 + -20x + x2 = 0 + -75
-20x + x2 = 0 + -75

Combine like terms: 0 + -75 = -75
-20x + x2 = -75

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = -75 + 100

Reorder the terms:
100 + -20x + x2 = -75 + 100

Combine like terms: -75 + 100 = 25
100 + -20x + x2 = 25

Factor a perfect square on the left side:
(x + -10)(x + -10) = 25

Calculate the square root of the right side: 5

Break this problem into two subproblems by setting 
(x + -10) equal to 5 and -5.

Subproblem 1

x + -10 = 5 Simplifying x + -10 = 5 Reorder the terms: -10 + x = 5 Solving -10 + x = 5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 5 + 10 Combine like terms: -10 + 10 = 0 0 + x = 5 + 10 x = 5 + 10 Combine like terms: 5 + 10 = 15 x = 15 Simplifying x = 15

Subproblem 2

x + -10 = -5 Simplifying x + -10 = -5 Reorder the terms: -10 + x = -5 Solving -10 + x = -5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -5 + 10 Combine like terms: -10 + 10 = 0 0 + x = -5 + 10 x = -5 + 10 Combine like terms: -5 + 10 = 5 x = 5 Simplifying x = 5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15, 5}

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