-8d^2+5d+9=0

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Solution for -8d^2+5d+9=0 equation: 


Simplifying
-8d2 + 5d + 9 = 0

Reorder the terms:
9 + 5d + -8d2 = 0

Solving
9 + 5d + -8d2 = 0

Solving for variable 'd'.

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-1.125 + -0.625d + d2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + -0.625d + 1.125 + d2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + -0.625d + d2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + -0.625d + d2 = 0 + 1.125
-0.625d + d2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
-0.625d + d2 = 1.125

The d term is -0.625d.  Take half its coefficient (-0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
-0.625d + 0.09765625 + d2 = 1.125 + 0.09765625

Reorder the terms:
0.09765625 + -0.625d + d2 = 1.125 + 0.09765625

Combine like terms: 1.125 + 0.09765625 = 1.22265625
0.09765625 + -0.625d + d2 = 1.22265625

Factor a perfect square on the left side:
(d + -0.3125)(d + -0.3125) = 1.22265625

Calculate the square root of the right side: 1.105737876

Break this problem into two subproblems by setting 
(d + -0.3125) equal to 1.105737876 and -1.105737876.


Subproblem 1
d + -0.3125 = 1.105737876

Simplifying
d + -0.3125 = 1.105737876

Reorder the terms:
-0.3125 + d = 1.105737876

Solving
-0.3125 + d = 1.105737876

Solving for variable 'd'.

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

Add '0.3125' to each side of the equation.
-0.3125 + 0.3125 + d = 1.105737876 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + d = 1.105737876 + 0.3125
d = 1.105737876 + 0.3125

Combine like terms: 1.105737876 + 0.3125 = 1.418237876
d = 1.418237876

Simplifying
d = 1.418237876


Subproblem 2
d + -0.3125 = -1.105737876

Simplifying
d + -0.3125 = -1.105737876

Reorder the terms:
-0.3125 + d = -1.105737876

Solving
-0.3125 + d = -1.105737876

Solving for variable 'd'.

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

Add '0.3125' to each side of the equation.
-0.3125 + 0.3125 + d = -1.105737876 + 0.3125

Combine like terms: -0.3125 + 0.3125 = 0.0000
0.0000 + d = -1.105737876 + 0.3125
d = -1.105737876 + 0.3125

Combine like terms: -1.105737876 + 0.3125 = -0.793237876
d = -0.793237876

Simplifying
d = -0.793237876


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {1.418237876, -0.793237876}

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