-.01x^2-.1x+42=0

Solution for -.01x^2-.1x+42=0 equation:

Simplifying
-0.01x2 + -0.1x + 42 = 0

Reorder the terms:
42 + -0.1x + -0.01x2 = 0

Solving
42 + -0.1x + -0.01x2 = 0

Solving for variable 'x'.

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

Divide each side by '-0.01'.
-4200 + 10x + x2 = 0

Move the constant term to the right:

Add '4200' to each side of the equation.
-4200 + 10x + 4200 + x2 = 0 + 4200

Reorder the terms:
-4200 + 4200 + 10x + x2 = 0 + 4200

Combine like terms: -4200 + 4200 = 0
0 + 10x + x2 = 0 + 4200
10x + x2 = 0 + 4200

Combine like terms: 0 + 4200 = 4200
10x + x2 = 4200

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 = 4200 + 25

Reorder the terms:
25 + 10x + x2 = 4200 + 25

Combine like terms: 4200 + 25 = 4225
25 + 10x + x2 = 4225

Factor a perfect square on the left side:
(x + 5)(x + 5) = 4225

Calculate the square root of the right side: 65

Break this problem into two subproblems by setting 
(x + 5) equal to 65 and -65.

Subproblem 1
x + 5 = 65

Simplifying
x + 5 = 65

Reorder the terms:
5 + x = 65

Solving
5 + x = 65

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 = 65 + -5

Combine like terms: 5 + -5 = 0
0 + x = 65 + -5
x = 65 + -5

Combine like terms: 65 + -5 = 60
x = 60

Simplifying
x = 60

Subproblem 2
x + 5 = -65

Simplifying
x + 5 = -65

Reorder the terms:
5 + x = -65

Solving
5 + x = -65

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 = -65 + -5

Combine like terms: 5 + -5 = 0
0 + x = -65 + -5
x = -65 + -5

Combine like terms: -65 + -5 = -70
x = -70

Simplifying
x = -70

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {60, -70}