=.01x^2-4x+300

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Solution for =.01x^2-4x+300 equation:


Simplifying
0 = 0.01x2 + -4x + 300

Reorder the terms:
0 = 300 + -4x + 0.01x2

Solving
0 = 300 + -4x + 0.01x2

Solving for variable 'x'.

Combine like terms: 0 + -300 = -300
-300 + 4x + -0.01x2 = 300 + -4x + 0.01x2 + -300 + 4x + -0.01x2

Reorder the terms:
-300 + 4x + -0.01x2 = 300 + -300 + -4x + 4x + 0.01x2 + -0.01x2

Combine like terms: 300 + -300 = 0
-300 + 4x + -0.01x2 = 0 + -4x + 4x + 0.01x2 + -0.01x2
-300 + 4x + -0.01x2 = -4x + 4x + 0.01x2 + -0.01x2

Combine like terms: -4x + 4x = 0
-300 + 4x + -0.01x2 = 0 + 0.01x2 + -0.01x2
-300 + 4x + -0.01x2 = 0.01x2 + -0.01x2

Combine like terms: 0.01x2 + -0.01x2 = 0.00
-300 + 4x + -0.01x2 = 0.00

Begin completing the square.  Divide all terms by
-0.01 the coefficient of the squared term: 

Divide each side by '-0.01'.
30000 + -400x + x2 = 0

Move the constant term to the right:

Add '-30000' to each side of the equation.
30000 + -400x + -30000 + x2 = 0 + -30000

Reorder the terms:
30000 + -30000 + -400x + x2 = 0 + -30000

Combine like terms: 30000 + -30000 = 0
0 + -400x + x2 = 0 + -30000
-400x + x2 = 0 + -30000

Combine like terms: 0 + -30000 = -30000
-400x + x2 = -30000

The x term is -400x.  Take half its coefficient (-200).
Square it (40000) and add it to both sides.

Add '40000' to each side of the equation.
-400x + 40000 + x2 = -30000 + 40000

Reorder the terms:
40000 + -400x + x2 = -30000 + 40000

Combine like terms: -30000 + 40000 = 10000
40000 + -400x + x2 = 10000

Factor a perfect square on the left side:
(x + -200)(x + -200) = 10000

Calculate the square root of the right side: 100

Break this problem into two subproblems by setting 
(x + -200) equal to 100 and -100.

Subproblem 1

x + -200 = 100 Simplifying x + -200 = 100 Reorder the terms: -200 + x = 100 Solving -200 + x = 100 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + x = 100 + 200 Combine like terms: -200 + 200 = 0 0 + x = 100 + 200 x = 100 + 200 Combine like terms: 100 + 200 = 300 x = 300 Simplifying x = 300

Subproblem 2

x + -200 = -100 Simplifying x + -200 = -100 Reorder the terms: -200 + x = -100 Solving -200 + x = -100 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '200' to each side of the equation. -200 + 200 + x = -100 + 200 Combine like terms: -200 + 200 = 0 0 + x = -100 + 200 x = -100 + 200 Combine like terms: -100 + 200 = 100 x = 100 Simplifying x = 100

Solution

The solution to the problem is based on the solutions from the subproblems. x = {300, 100}

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