0.003x^2+0.03x-9=0

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Solution for 0.003x^2+0.03x-9=0 equation:


Simplifying
0.003x2 + 0.03x + -9 = 0

Reorder the terms:
-9 + 0.03x + 0.003x2 = 0

Solving
-9 + 0.03x + 0.003x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.003'.
-3000 + 10x + x2 = 0

Move the constant term to the right:

Add '3000' to each side of the equation.
-3000 + 10x + 3000 + x2 = 0 + 3000

Reorder the terms:
-3000 + 3000 + 10x + x2 = 0 + 3000

Combine like terms: -3000 + 3000 = 0
0 + 10x + x2 = 0 + 3000
10x + x2 = 0 + 3000

Combine like terms: 0 + 3000 = 3000
10x + x2 = 3000

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = 3000 + 25

Reorder the terms:
25 + 10x + x2 = 3000 + 25

Combine like terms: 3000 + 25 = 3025
25 + 10x + x2 = 3025

Factor a perfect square on the left side:
(x + 5)(x + 5) = 3025

Calculate the square root of the right side: 55

Break this problem into two subproblems by setting 
(x + 5) equal to 55 and -55.

Subproblem 1

x + 5 = 55 Simplifying x + 5 = 55 Reorder the terms: 5 + x = 55 Solving 5 + x = 55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 55 + -5 Combine like terms: 5 + -5 = 0 0 + x = 55 + -5 x = 55 + -5 Combine like terms: 55 + -5 = 50 x = 50 Simplifying x = 50

Subproblem 2

x + 5 = -55 Simplifying x + 5 = -55 Reorder the terms: 5 + x = -55 Solving 5 + x = -55 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -55 + -5 Combine like terms: 5 + -5 = 0 0 + x = -55 + -5 x = -55 + -5 Combine like terms: -55 + -5 = -60 x = -60 Simplifying x = -60

Solution

The solution to the problem is based on the solutions from the subproblems. x = {50, -60}

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