.005x^2+.002x-9=0

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Solution for .005x^2+.002x-9=0 equation:


Simplifying
0.005x2 + 0.002x + -9 = 0

Reorder the terms:
-9 + 0.002x + 0.005x2 = 0

Solving
-9 + 0.002x + 0.005x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.005'.
-1800 + 0.4x + x2 = 0

Move the constant term to the right:

Add '1800' to each side of the equation.
-1800 + 0.4x + 1800 + x2 = 0 + 1800

Reorder the terms:
-1800 + 1800 + 0.4x + x2 = 0 + 1800

Combine like terms: -1800 + 1800 = 0
0 + 0.4x + x2 = 0 + 1800
0.4x + x2 = 0 + 1800

Combine like terms: 0 + 1800 = 1800
0.4x + x2 = 1800

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = 1800 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 1800 + 0.04

Combine like terms: 1800 + 0.04 = 1800.04
0.04 + 0.4x + x2 = 1800.04

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 1800.04

Calculate the square root of the right side: 42.426878273

Break this problem into two subproblems by setting 
(x + 0.2) equal to 42.426878273 and -42.426878273.

Subproblem 1

x + 0.2 = 42.426878273 Simplifying x + 0.2 = 42.426878273 Reorder the terms: 0.2 + x = 42.426878273 Solving 0.2 + x = 42.426878273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 42.426878273 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 42.426878273 + -0.2 x = 42.426878273 + -0.2 Combine like terms: 42.426878273 + -0.2 = 42.226878273 x = 42.226878273 Simplifying x = 42.226878273

Subproblem 2

x + 0.2 = -42.426878273 Simplifying x + 0.2 = -42.426878273 Reorder the terms: 0.2 + x = -42.426878273 Solving 0.2 + x = -42.426878273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -42.426878273 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -42.426878273 + -0.2 x = -42.426878273 + -0.2 Combine like terms: -42.426878273 + -0.2 = -42.626878273 x = -42.626878273 Simplifying x = -42.626878273

Solution

The solution to the problem is based on the solutions from the subproblems. x = {42.226878273, -42.626878273}

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