0.0001x^2+.05x-1.6=0

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Solution for 0.0001x^2+.05x-1.6=0 equation:


Simplifying
0.0001x2 + 0.05x + -1.6 = 0

Reorder the terms:
-1.6 + 0.05x + 0.0001x2 = 0

Solving
-1.6 + 0.05x + 0.0001x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.0001 the coefficient of the squared term: 

Divide each side by '0.0001'.
-16000 + 500x + x2 = 0

Move the constant term to the right:

Add '16000' to each side of the equation.
-16000 + 500x + 16000 + x2 = 0 + 16000

Reorder the terms:
-16000 + 16000 + 500x + x2 = 0 + 16000

Combine like terms: -16000 + 16000 = 0
0 + 500x + x2 = 0 + 16000
500x + x2 = 0 + 16000

Combine like terms: 0 + 16000 = 16000
500x + x2 = 16000

The x term is 500x.  Take half its coefficient (250).
Square it (62500) and add it to both sides.

Add '62500' to each side of the equation.
500x + 62500 + x2 = 16000 + 62500

Reorder the terms:
62500 + 500x + x2 = 16000 + 62500

Combine like terms: 16000 + 62500 = 78500
62500 + 500x + x2 = 78500

Factor a perfect square on the left side:
(x + 250)(x + 250) = 78500

Calculate the square root of the right side: 280.178514522

Break this problem into two subproblems by setting 
(x + 250) equal to 280.178514522 and -280.178514522.

Subproblem 1

x + 250 = 280.178514522 Simplifying x + 250 = 280.178514522 Reorder the terms: 250 + x = 280.178514522 Solving 250 + x = 280.178514522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = 280.178514522 + -250 Combine like terms: 250 + -250 = 0 0 + x = 280.178514522 + -250 x = 280.178514522 + -250 Combine like terms: 280.178514522 + -250 = 30.178514522 x = 30.178514522 Simplifying x = 30.178514522

Subproblem 2

x + 250 = -280.178514522 Simplifying x + 250 = -280.178514522 Reorder the terms: 250 + x = -280.178514522 Solving 250 + x = -280.178514522 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = -280.178514522 + -250 Combine like terms: 250 + -250 = 0 0 + x = -280.178514522 + -250 x = -280.178514522 + -250 Combine like terms: -280.178514522 + -250 = -530.178514522 x = -530.178514522 Simplifying x = -530.178514522

Solution

The solution to the problem is based on the solutions from the subproblems. x = {30.178514522, -530.178514522}

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