-0.02d^2+0.4d+1=0

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Solution for -0.02d^2+0.4d+1=0 equation: 


Simplifying
-0.02d2 + 0.4d + 1 = 0

Reorder the terms:
1 + 0.4d + -0.02d2 = 0

Solving
1 + 0.4d + -0.02d2 = 0

Solving for variable 'd'.

Begin completing the square.  Divide all terms by
-0.02 the coefficient of the squared term: 

Divide each side by '-0.02'.
-50 + -20d + d2 = 0

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -20d + 50 + d2 = 0 + 50

Reorder the terms:
-50 + 50 + -20d + d2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -20d + d2 = 0 + 50
-20d + d2 = 0 + 50

Combine like terms: 0 + 50 = 50
-20d + d2 = 50

The d term is -20d.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20d + 100 + d2 = 50 + 100

Reorder the terms:
100 + -20d + d2 = 50 + 100

Combine like terms: 50 + 100 = 150
100 + -20d + d2 = 150

Factor a perfect square on the left side:
(d + -10)(d + -10) = 150

Calculate the square root of the right side: 12.247448714

Break this problem into two subproblems by setting 
(d + -10) equal to 12.247448714 and -12.247448714.


Subproblem 1
d + -10 = 12.247448714

Simplifying
d + -10 = 12.247448714

Reorder the terms:
-10 + d = 12.247448714

Solving
-10 + d = 12.247448714

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '10' to each side of the equation.
-10 + 10 + d = 12.247448714 + 10

Combine like terms: -10 + 10 = 0
0 + d = 12.247448714 + 10
d = 12.247448714 + 10

Combine like terms: 12.247448714 + 10 = 22.247448714
d = 22.247448714

Simplifying
d = 22.247448714


Subproblem 2
d + -10 = -12.247448714

Simplifying
d + -10 = -12.247448714

Reorder the terms:
-10 + d = -12.247448714

Solving
-10 + d = -12.247448714

Solving for variable 'd'.

Move all terms containing d to the left, all other terms to the right.

Add '10' to each side of the equation.
-10 + 10 + d = -12.247448714 + 10

Combine like terms: -10 + 10 = 0
0 + d = -12.247448714 + 10
d = -12.247448714 + 10

Combine like terms: -12.247448714 + 10 = -2.247448714
d = -2.247448714

Simplifying
d = -2.247448714


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {22.247448714, -2.247448714}

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