d^2+d-40=

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Solution for d^2+d-40= equation: 


Simplifying
d2 + d + -40 = 0

Reorder the terms:
-40 + d + d2 = 0

Solving
-40 + d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + d + 40 + d2 = 0 + 40

Reorder the terms:
-40 + 40 + d + d2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + d + d2 = 0 + 40
d + d2 = 0 + 40

Combine like terms: 0 + 40 = 40
d + d2 = 40

The d term is d.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
d + 0.25 + d2 = 40 + 0.25

Reorder the terms:
0.25 + d + d2 = 40 + 0.25

Combine like terms: 40 + 0.25 = 40.25
0.25 + d + d2 = 40.25

Factor a perfect square on the left side:
(d + 0.5)(d + 0.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(d + 0.5) equal to 6.34428877 and -6.34428877.


Subproblem 1
d + 0.5 = 6.34428877

Simplifying
d + 0.5 = 6.34428877

Reorder the terms:
0.5 + d = 6.34428877

Solving
0.5 + d = 6.34428877

Solving for variable 'd'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + d = 6.34428877 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + d = 6.34428877 + -0.5
d = 6.34428877 + -0.5

Combine like terms: 6.34428877 + -0.5 = 5.84428877
d = 5.84428877

Simplifying
d = 5.84428877


Subproblem 2
d + 0.5 = -6.34428877

Simplifying
d + 0.5 = -6.34428877

Reorder the terms:
0.5 + d = -6.34428877

Solving
0.5 + d = -6.34428877

Solving for variable 'd'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + d = -6.34428877 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + d = -6.34428877 + -0.5
d = -6.34428877 + -0.5

Combine like terms: -6.34428877 + -0.5 = -6.84428877
d = -6.84428877

Simplifying
d = -6.84428877


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {5.84428877, -6.84428877}

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