(q-1)(q-3)=2

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Solution for (q-1)(q-3)=2 equation:


Simplifying
(q + -1)(q + -3) = 2

Reorder the terms:
(-1 + q)(q + -3) = 2

Reorder the terms:
(-1 + q)(-3 + q) = 2

Multiply (-1 + q) * (-3 + q)
(-1(-3 + q) + q(-3 + q)) = 2
((-3 * -1 + q * -1) + q(-3 + q)) = 2
((3 + -1q) + q(-3 + q)) = 2
(3 + -1q + (-3 * q + q * q)) = 2
(3 + -1q + (-3q + q2)) = 2

Combine like terms: -1q + -3q = -4q
(3 + -4q + q2) = 2

Solving
3 + -4q + q2 = 2

Solving for variable 'q'.

Reorder the terms:
3 + -2 + -4q + q2 = 2 + -2

Combine like terms: 3 + -2 = 1
1 + -4q + q2 = 2 + -2

Combine like terms: 2 + -2 = 0
1 + -4q + q2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -4q + -1 + q2 = 0 + -1

Reorder the terms:
1 + -1 + -4q + q2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4q + q2 = 0 + -1
-4q + q2 = 0 + -1

Combine like terms: 0 + -1 = -1
-4q + q2 = -1

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

Add '4' to each side of the equation.
-4q + 4 + q2 = -1 + 4

Reorder the terms:
4 + -4q + q2 = -1 + 4

Combine like terms: -1 + 4 = 3
4 + -4q + q2 = 3

Factor a perfect square on the left side:
(q + -2)(q + -2) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(q + -2) equal to 1.732050808 and -1.732050808.

Subproblem 1

q + -2 = 1.732050808 Simplifying q + -2 = 1.732050808 Reorder the terms: -2 + q = 1.732050808 Solving -2 + q = 1.732050808 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + q = 1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + q = 1.732050808 + 2 q = 1.732050808 + 2 Combine like terms: 1.732050808 + 2 = 3.732050808 q = 3.732050808 Simplifying q = 3.732050808

Subproblem 2

q + -2 = -1.732050808 Simplifying q + -2 = -1.732050808 Reorder the terms: -2 + q = -1.732050808 Solving -2 + q = -1.732050808 Solving for variable 'q'. Move all terms containing q to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + q = -1.732050808 + 2 Combine like terms: -2 + 2 = 0 0 + q = -1.732050808 + 2 q = -1.732050808 + 2 Combine like terms: -1.732050808 + 2 = 0.267949192 q = 0.267949192 Simplifying q = 0.267949192

Solution

The solution to the problem is based on the solutions from the subproblems. q = {3.732050808, 0.267949192}

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