d^2+50d-8=0

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Solution for d^2+50d-8=0 equation: 


Simplifying
d2 + 50d + -8 = 0

Reorder the terms:
-8 + 50d + d2 = 0

Solving
-8 + 50d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 50d + 8 + d2 = 0 + 8

Reorder the terms:
-8 + 8 + 50d + d2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 50d + d2 = 0 + 8
50d + d2 = 0 + 8

Combine like terms: 0 + 8 = 8
50d + d2 = 8

The d term is 50d.  Take half its coefficient (25).
Square it (625) and add it to both sides.

Add '625' to each side of the equation.
50d + 625 + d2 = 8 + 625

Reorder the terms:
625 + 50d + d2 = 8 + 625

Combine like terms: 8 + 625 = 633
625 + 50d + d2 = 633

Factor a perfect square on the left side:
(d + 25)(d + 25) = 633

Calculate the square root of the right side: 25.159491251

Break this problem into two subproblems by setting 
(d + 25) equal to 25.159491251 and -25.159491251.


Subproblem 1
d + 25 = 25.159491251

Simplifying
d + 25 = 25.159491251

Reorder the terms:
25 + d = 25.159491251

Solving
25 + d = 25.159491251

Solving for variable 'd'.

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

Add '-25' to each side of the equation.
25 + -25 + d = 25.159491251 + -25

Combine like terms: 25 + -25 = 0
0 + d = 25.159491251 + -25
d = 25.159491251 + -25

Combine like terms: 25.159491251 + -25 = 0.159491251
d = 0.159491251

Simplifying
d = 0.159491251


Subproblem 2
d + 25 = -25.159491251

Simplifying
d + 25 = -25.159491251

Reorder the terms:
25 + d = -25.159491251

Solving
25 + d = -25.159491251

Solving for variable 'd'.

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

Add '-25' to each side of the equation.
25 + -25 + d = -25.159491251 + -25

Combine like terms: 25 + -25 = 0
0 + d = -25.159491251 + -25
d = -25.159491251 + -25

Combine like terms: -25.159491251 + -25 = -50.159491251
d = -50.159491251

Simplifying
d = -50.159491251


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {0.159491251, -50.159491251}

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