16d^2+40d-25=9

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Solution for 16d^2+40d-25=9 equation: 


Simplifying
16d2 + 40d + -25 = 9

Reorder the terms:
-25 + 40d + 16d2 = 9

Solving
-25 + 40d + 16d2 = 9

Solving for variable 'd'.

Reorder the terms:
-25 + -9 + 40d + 16d2 = 9 + -9

Combine like terms: -25 + -9 = -34
-34 + 40d + 16d2 = 9 + -9

Combine like terms: 9 + -9 = 0
-34 + 40d + 16d2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + 20d + 8d2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-17 + 20d + 8d2)' equal to zero and attempt to solve:

Simplifying
-17 + 20d + 8d2 = 0

Solving
-17 + 20d + 8d2 = 0

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

Divide each side by '8'.
-2.125 + 2.5d + d2 = 0

Move the constant term to the right:

Add '2.125' to each side of the equation.
-2.125 + 2.5d + 2.125 + d2 = 0 + 2.125

Reorder the terms:
-2.125 + 2.125 + 2.5d + d2 = 0 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + 2.5d + d2 = 0 + 2.125
2.5d + d2 = 0 + 2.125

Combine like terms: 0 + 2.125 = 2.125
2.5d + d2 = 2.125

The d term is 2.5d.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5d + 1.5625 + d2 = 2.125 + 1.5625

Reorder the terms:
1.5625 + 2.5d + d2 = 2.125 + 1.5625

Combine like terms: 2.125 + 1.5625 = 3.6875
1.5625 + 2.5d + d2 = 3.6875

Factor a perfect square on the left side:
(d + 1.25)(d + 1.25) = 3.6875

Calculate the square root of the right side: 1.920286437

Break this problem into two subproblems by setting 
(d + 1.25) equal to 1.920286437 and -1.920286437.


Subproblem 1
d + 1.25 = 1.920286437

Simplifying
d + 1.25 = 1.920286437

Reorder the terms:
1.25 + d = 1.920286437

Solving
1.25 + d = 1.920286437

Solving for variable 'd'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + d = 1.920286437 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + d = 1.920286437 + -1.25
d = 1.920286437 + -1.25

Combine like terms: 1.920286437 + -1.25 = 0.670286437
d = 0.670286437

Simplifying
d = 0.670286437


Subproblem 2
d + 1.25 = -1.920286437

Simplifying
d + 1.25 = -1.920286437

Reorder the terms:
1.25 + d = -1.920286437

Solving
1.25 + d = -1.920286437

Solving for variable 'd'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + d = -1.920286437 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + d = -1.920286437 + -1.25
d = -1.920286437 + -1.25

Combine like terms: -1.920286437 + -1.25 = -3.170286437
d = -3.170286437

Simplifying
d = -3.170286437


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {0.670286437, -3.170286437}
Solution
d = {0.670286437, -3.170286437}

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