.80x(x-100)=450

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Solution for .80x(x-100)=450 equation:


Simplifying
0.80x(x + -100) = 450

Reorder the terms:
0.80x(-100 + x) = 450
(-100 * 0.80x + x * 0.80x) = 450
(-80x + 0.80x2) = 450

Solving
-80x + 0.80x2 = 450

Solving for variable 'x'.

Reorder the terms:
-450 + -80x + 0.80x2 = 450 + -450

Combine like terms: 450 + -450 = 0
-450 + -80x + 0.80x2 = 0

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

Divide each side by '0.80'.
-562.5 + -100x + x2 = 0

Move the constant term to the right:

Add '562.5' to each side of the equation.
-562.5 + -100x + 562.5 + x2 = 0 + 562.5

Reorder the terms:
-562.5 + 562.5 + -100x + x2 = 0 + 562.5

Combine like terms: -562.5 + 562.5 = 0.0
0.0 + -100x + x2 = 0 + 562.5
-100x + x2 = 0 + 562.5

Combine like terms: 0 + 562.5 = 562.5
-100x + x2 = 562.5

The x term is -100x.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100x + 2500 + x2 = 562.5 + 2500

Reorder the terms:
2500 + -100x + x2 = 562.5 + 2500

Combine like terms: 562.5 + 2500 = 3062.5
2500 + -100x + x2 = 3062.5

Factor a perfect square on the left side:
(x + -50)(x + -50) = 3062.5

Calculate the square root of the right side: 55.339859053

Break this problem into two subproblems by setting 
(x + -50) equal to 55.339859053 and -55.339859053.

Subproblem 1

x + -50 = 55.339859053 Simplifying x + -50 = 55.339859053 Reorder the terms: -50 + x = 55.339859053 Solving -50 + x = 55.339859053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 55.339859053 + 50 Combine like terms: -50 + 50 = 0 0 + x = 55.339859053 + 50 x = 55.339859053 + 50 Combine like terms: 55.339859053 + 50 = 105.339859053 x = 105.339859053 Simplifying x = 105.339859053

Subproblem 2

x + -50 = -55.339859053 Simplifying x + -50 = -55.339859053 Reorder the terms: -50 + x = -55.339859053 Solving -50 + x = -55.339859053 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -55.339859053 + 50 Combine like terms: -50 + 50 = 0 0 + x = -55.339859053 + 50 x = -55.339859053 + 50 Combine like terms: -55.339859053 + 50 = -5.339859053 x = -5.339859053 Simplifying x = -5.339859053

Solution

The solution to the problem is based on the solutions from the subproblems. x = {105.339859053, -5.339859053}

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