d^2-28d=9

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Solution for d^2-28d=9 equation:


Simplifying
d2 + -28d = 9

Reorder the terms:
-28d + d2 = 9

Solving
-28d + d2 = 9

Solving for variable 'd'.

Reorder the terms:
-9 + -28d + d2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + -28d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -28d + 9 + d2 = 0 + 9

Reorder the terms:
-9 + 9 + -28d + d2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -28d + d2 = 0 + 9
-28d + d2 = 0 + 9

Combine like terms: 0 + 9 = 9
-28d + d2 = 9

The d term is -28d.  Take half its coefficient (-14).
Square it (196) and add it to both sides.

Add '196' to each side of the equation.
-28d + 196 + d2 = 9 + 196

Reorder the terms:
196 + -28d + d2 = 9 + 196

Combine like terms: 9 + 196 = 205
196 + -28d + d2 = 205

Factor a perfect square on the left side:
(d + -14)(d + -14) = 205

Calculate the square root of the right side: 14.317821063

Break this problem into two subproblems by setting 
(d + -14) equal to 14.317821063 and -14.317821063.

Subproblem 1

d + -14 = 14.317821063 Simplifying d + -14 = 14.317821063 Reorder the terms: -14 + d = 14.317821063 Solving -14 + d = 14.317821063 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + d = 14.317821063 + 14 Combine like terms: -14 + 14 = 0 0 + d = 14.317821063 + 14 d = 14.317821063 + 14 Combine like terms: 14.317821063 + 14 = 28.317821063 d = 28.317821063 Simplifying d = 28.317821063

Subproblem 2

d + -14 = -14.317821063 Simplifying d + -14 = -14.317821063 Reorder the terms: -14 + d = -14.317821063 Solving -14 + d = -14.317821063 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + d = -14.317821063 + 14 Combine like terms: -14 + 14 = 0 0 + d = -14.317821063 + 14 d = -14.317821063 + 14 Combine like terms: -14.317821063 + 14 = -0.317821063 d = -0.317821063 Simplifying d = -0.317821063

Solution

The solution to the problem is based on the solutions from the subproblems. d = {28.317821063, -0.317821063}

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