55=(9-d)11d

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Solution for 55=(9-d)11d equation:


Simplifying
55 = (9 + -1d) * 11d

Reorder the terms for easier multiplication:
55 = 11d(9 + -1d)
55 = (9 * 11d + -1d * 11d)
55 = (99d + -11d2)

Solving
55 = 99d + -11d2

Solving for variable 'd'.

Reorder the terms:
55 + -99d + 11d2 = 99d + -99d + -11d2 + 11d2

Combine like terms: 99d + -99d = 0
55 + -99d + 11d2 = 0 + -11d2 + 11d2
55 + -99d + 11d2 = -11d2 + 11d2

Combine like terms: -11d2 + 11d2 = 0
55 + -99d + 11d2 = 0

Factor out the Greatest Common Factor (GCF), '11'.
11(5 + -9d + d2) = 0

Ignore the factor 11.

Subproblem 1

Set the factor '(5 + -9d + d2)' equal to zero and attempt to solve: Simplifying 5 + -9d + d2 = 0 Solving 5 + -9d + d2 = 0 Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -9d + -5 + d2 = 0 + -5 Reorder the terms: 5 + -5 + -9d + d2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9d + d2 = 0 + -5 -9d + d2 = 0 + -5 Combine like terms: 0 + -5 = -5 -9d + d2 = -5 The d term is -9d. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9d + 20.25 + d2 = -5 + 20.25 Reorder the terms: 20.25 + -9d + d2 = -5 + 20.25 Combine like terms: -5 + 20.25 = 15.25 20.25 + -9d + d2 = 15.25 Factor a perfect square on the left side: (d + -4.5)(d + -4.5) = 15.25 Calculate the square root of the right side: 3.905124838 Break this problem into two subproblems by setting (d + -4.5) equal to 3.905124838 and -3.905124838.

Subproblem 1

d + -4.5 = 3.905124838 Simplifying d + -4.5 = 3.905124838 Reorder the terms: -4.5 + d = 3.905124838 Solving -4.5 + d = 3.905124838 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + d = 3.905124838 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + d = 3.905124838 + 4.5 d = 3.905124838 + 4.5 Combine like terms: 3.905124838 + 4.5 = 8.405124838 d = 8.405124838 Simplifying d = 8.405124838

Subproblem 2

d + -4.5 = -3.905124838 Simplifying d + -4.5 = -3.905124838 Reorder the terms: -4.5 + d = -3.905124838 Solving -4.5 + d = -3.905124838 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + d = -3.905124838 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + d = -3.905124838 + 4.5 d = -3.905124838 + 4.5 Combine like terms: -3.905124838 + 4.5 = 0.594875162 d = 0.594875162 Simplifying d = 0.594875162

Solution

The solution to the problem is based on the solutions from the subproblems. d = {8.405124838, 0.594875162}

Solution

d = {8.405124838, 0.594875162}

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