(d-3)(d-1)=4

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Solution for (d-3)(d-1)=4 equation:


Simplifying
(d + -3)(d + -1) = 4

Reorder the terms:
(-3 + d)(d + -1) = 4

Reorder the terms:
(-3 + d)(-1 + d) = 4

Multiply (-3 + d) * (-1 + d)
(-3(-1 + d) + d(-1 + d)) = 4
((-1 * -3 + d * -3) + d(-1 + d)) = 4
((3 + -3d) + d(-1 + d)) = 4
(3 + -3d + (-1 * d + d * d)) = 4
(3 + -3d + (-1d + d2)) = 4

Combine like terms: -3d + -1d = -4d
(3 + -4d + d2) = 4

Solving
3 + -4d + d2 = 4

Solving for variable 'd'.

Reorder the terms:
3 + -4 + -4d + d2 = 4 + -4

Combine like terms: 3 + -4 = -1
-1 + -4d + d2 = 4 + -4

Combine like terms: 4 + -4 = 0
-1 + -4d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -4d + 1 + d2 = 0 + 1

Reorder the terms:
-1 + 1 + -4d + d2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4d + d2 = 0 + 1
-4d + d2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4d + d2 = 1

The d term is -4d.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4d + 4 + d2 = 1 + 4

Reorder the terms:
4 + -4d + d2 = 1 + 4

Combine like terms: 1 + 4 = 5
4 + -4d + d2 = 5

Factor a perfect square on the left side:
(d + -2)(d + -2) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(d + -2) equal to 2.236067978 and -2.236067978.

Subproblem 1

d + -2 = 2.236067978 Simplifying d + -2 = 2.236067978 Reorder the terms: -2 + d = 2.236067978 Solving -2 + d = 2.236067978 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + d = 2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + d = 2.236067978 + 2 d = 2.236067978 + 2 Combine like terms: 2.236067978 + 2 = 4.236067978 d = 4.236067978 Simplifying d = 4.236067978

Subproblem 2

d + -2 = -2.236067978 Simplifying d + -2 = -2.236067978 Reorder the terms: -2 + d = -2.236067978 Solving -2 + d = -2.236067978 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + d = -2.236067978 + 2 Combine like terms: -2 + 2 = 0 0 + d = -2.236067978 + 2 d = -2.236067978 + 2 Combine like terms: -2.236067978 + 2 = -0.236067978 d = -0.236067978 Simplifying d = -0.236067978

Solution

The solution to the problem is based on the solutions from the subproblems. d = {4.236067978, -0.236067978}

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