.04(x-50)(x-150)=0

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Solution for .04(x-50)(x-150)=0 equation:


Simplifying
0.04(x + -50)(x + -150) = 0

Reorder the terms:
0.04(-50 + x)(x + -150) = 0

Reorder the terms:
0.04(-50 + x)(-150 + x) = 0

Multiply (-50 + x) * (-150 + x)
0.04(-50(-150 + x) + x(-150 + x)) = 0
0.04((-150 * -50 + x * -50) + x(-150 + x)) = 0
0.04((7500 + -50x) + x(-150 + x)) = 0
0.04(7500 + -50x + (-150 * x + x * x)) = 0
0.04(7500 + -50x + (-150x + x2)) = 0

Combine like terms: -50x + -150x = -200x
0.04(7500 + -200x + x2) = 0
(7500 * 0.04 + -200x * 0.04 + x2 * 0.04) = 0
(300 + -8x + 0.04x2) = 0

Solving
300 + -8x + 0.04x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.04'.
7500 + -200x + x2 = 0

Move the constant term to the right:

Add '-7500' to each side of the equation.
7500 + -200x + -7500 + x2 = 0 + -7500

Reorder the terms:
7500 + -7500 + -200x + x2 = 0 + -7500

Combine like terms: 7500 + -7500 = 0
0 + -200x + x2 = 0 + -7500
-200x + x2 = 0 + -7500

Combine like terms: 0 + -7500 = -7500
-200x + x2 = -7500

The x term is -200x.  Take half its coefficient (-100).
Square it (10000) and add it to both sides.

Add '10000' to each side of the equation.
-200x + 10000 + x2 = -7500 + 10000

Reorder the terms:
10000 + -200x + x2 = -7500 + 10000

Combine like terms: -7500 + 10000 = 2500
10000 + -200x + x2 = 2500

Factor a perfect square on the left side:
(x + -100)(x + -100) = 2500

Calculate the square root of the right side: 50

Break this problem into two subproblems by setting 
(x + -100) equal to 50 and -50.

Subproblem 1

x + -100 = 50 Simplifying x + -100 = 50 Reorder the terms: -100 + x = 50 Solving -100 + x = 50 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 50 + 100 Combine like terms: -100 + 100 = 0 0 + x = 50 + 100 x = 50 + 100 Combine like terms: 50 + 100 = 150 x = 150 Simplifying x = 150

Subproblem 2

x + -100 = -50 Simplifying x + -100 = -50 Reorder the terms: -100 + x = -50 Solving -100 + x = -50 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -50 + 100 Combine like terms: -100 + 100 = 0 0 + x = -50 + 100 x = -50 + 100 Combine like terms: -50 + 100 = 50 x = 50 Simplifying x = 50

Solution

The solution to the problem is based on the solutions from the subproblems. x = {150, 50}

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