(r-2)(r+6)=29

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Solution for (r-2)(r+6)=29 equation:


Simplifying
(r + -2)(r + 6) = 29

Reorder the terms:
(-2 + r)(r + 6) = 29

Reorder the terms:
(-2 + r)(6 + r) = 29

Multiply (-2 + r) * (6 + r)
(-2(6 + r) + r(6 + r)) = 29
((6 * -2 + r * -2) + r(6 + r)) = 29
((-12 + -2r) + r(6 + r)) = 29
(-12 + -2r + (6 * r + r * r)) = 29
(-12 + -2r + (6r + r2)) = 29

Combine like terms: -2r + 6r = 4r
(-12 + 4r + r2) = 29

Solving
-12 + 4r + r2 = 29

Solving for variable 'r'.

Reorder the terms:
-12 + -29 + 4r + r2 = 29 + -29

Combine like terms: -12 + -29 = -41
-41 + 4r + r2 = 29 + -29

Combine like terms: 29 + -29 = 0
-41 + 4r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '41' to each side of the equation.
-41 + 4r + 41 + r2 = 0 + 41

Reorder the terms:
-41 + 41 + 4r + r2 = 0 + 41

Combine like terms: -41 + 41 = 0
0 + 4r + r2 = 0 + 41
4r + r2 = 0 + 41

Combine like terms: 0 + 41 = 41
4r + r2 = 41

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

Add '4' to each side of the equation.
4r + 4 + r2 = 41 + 4

Reorder the terms:
4 + 4r + r2 = 41 + 4

Combine like terms: 41 + 4 = 45
4 + 4r + r2 = 45

Factor a perfect square on the left side:
(r + 2)(r + 2) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(r + 2) equal to 6.708203933 and -6.708203933.

Subproblem 1

r + 2 = 6.708203933 Simplifying r + 2 = 6.708203933 Reorder the terms: 2 + r = 6.708203933 Solving 2 + r = 6.708203933 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = 6.708203933 + -2 Combine like terms: 2 + -2 = 0 0 + r = 6.708203933 + -2 r = 6.708203933 + -2 Combine like terms: 6.708203933 + -2 = 4.708203933 r = 4.708203933 Simplifying r = 4.708203933

Subproblem 2

r + 2 = -6.708203933 Simplifying r + 2 = -6.708203933 Reorder the terms: 2 + r = -6.708203933 Solving 2 + r = -6.708203933 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + r = -6.708203933 + -2 Combine like terms: 2 + -2 = 0 0 + r = -6.708203933 + -2 r = -6.708203933 + -2 Combine like terms: -6.708203933 + -2 = -8.708203933 r = -8.708203933 Simplifying r = -8.708203933

Solution

The solution to the problem is based on the solutions from the subproblems. r = {4.708203933, -8.708203933}

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