d^2-30d-280=0

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Solution for d^2-30d-280=0 equation: 


Simplifying
d2 + -30d + -280 = 0

Reorder the terms:
-280 + -30d + d2 = 0

Solving
-280 + -30d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '280' to each side of the equation.
-280 + -30d + 280 + d2 = 0 + 280

Reorder the terms:
-280 + 280 + -30d + d2 = 0 + 280

Combine like terms: -280 + 280 = 0
0 + -30d + d2 = 0 + 280
-30d + d2 = 0 + 280

Combine like terms: 0 + 280 = 280
-30d + d2 = 280

The d term is -30d.  Take half its coefficient (-15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
-30d + 225 + d2 = 280 + 225

Reorder the terms:
225 + -30d + d2 = 280 + 225

Combine like terms: 280 + 225 = 505
225 + -30d + d2 = 505

Factor a perfect square on the left side:
(d + -15)(d + -15) = 505

Calculate the square root of the right side: 22.472205054

Break this problem into two subproblems by setting 
(d + -15) equal to 22.472205054 and -22.472205054.


Subproblem 1
d + -15 = 22.472205054

Simplifying
d + -15 = 22.472205054

Reorder the terms:
-15 + d = 22.472205054

Solving
-15 + d = 22.472205054

Solving for variable 'd'.

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

Add '15' to each side of the equation.
-15 + 15 + d = 22.472205054 + 15

Combine like terms: -15 + 15 = 0
0 + d = 22.472205054 + 15
d = 22.472205054 + 15

Combine like terms: 22.472205054 + 15 = 37.472205054
d = 37.472205054

Simplifying
d = 37.472205054


Subproblem 2
d + -15 = -22.472205054

Simplifying
d + -15 = -22.472205054

Reorder the terms:
-15 + d = -22.472205054

Solving
-15 + d = -22.472205054

Solving for variable 'd'.

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

Add '15' to each side of the equation.
-15 + 15 + d = -22.472205054 + 15

Combine like terms: -15 + 15 = 0
0 + d = -22.472205054 + 15
d = -22.472205054 + 15

Combine like terms: -22.472205054 + 15 = -7.472205054
d = -7.472205054

Simplifying
d = -7.472205054


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {37.472205054, -7.472205054}

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