(r-2)(r+10)=9

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Solution for (r-2)(r+10)=9 equation:


Simplifying
(r + -2)(r + 10) = 9

Reorder the terms:
(-2 + r)(r + 10) = 9

Reorder the terms:
(-2 + r)(10 + r) = 9

Multiply (-2 + r) * (10 + r)
(-2(10 + r) + r(10 + r)) = 9
((10 * -2 + r * -2) + r(10 + r)) = 9
((-20 + -2r) + r(10 + r)) = 9
(-20 + -2r + (10 * r + r * r)) = 9
(-20 + -2r + (10r + r2)) = 9

Combine like terms: -2r + 10r = 8r
(-20 + 8r + r2) = 9

Solving
-20 + 8r + r2 = 9

Solving for variable 'r'.

Reorder the terms:
-20 + -9 + 8r + r2 = 9 + -9

Combine like terms: -20 + -9 = -29
-29 + 8r + r2 = 9 + -9

Combine like terms: 9 + -9 = 0
-29 + 8r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 8r + 29 + r2 = 0 + 29

Reorder the terms:
-29 + 29 + 8r + r2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 8r + r2 = 0 + 29
8r + r2 = 0 + 29

Combine like terms: 0 + 29 = 29
8r + r2 = 29

The r term is 8r.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8r + 16 + r2 = 29 + 16

Reorder the terms:
16 + 8r + r2 = 29 + 16

Combine like terms: 29 + 16 = 45
16 + 8r + r2 = 45

Factor a perfect square on the left side:
(r + 4)(r + 4) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(r + 4) equal to 6.708203933 and -6.708203933.

Subproblem 1

r + 4 = 6.708203933 Simplifying r + 4 = 6.708203933 Reorder the terms: 4 + r = 6.708203933 Solving 4 + r = 6.708203933 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = 6.708203933 + -4 Combine like terms: 4 + -4 = 0 0 + r = 6.708203933 + -4 r = 6.708203933 + -4 Combine like terms: 6.708203933 + -4 = 2.708203933 r = 2.708203933 Simplifying r = 2.708203933

Subproblem 2

r + 4 = -6.708203933 Simplifying r + 4 = -6.708203933 Reorder the terms: 4 + r = -6.708203933 Solving 4 + r = -6.708203933 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + r = -6.708203933 + -4 Combine like terms: 4 + -4 = 0 0 + r = -6.708203933 + -4 r = -6.708203933 + -4 Combine like terms: -6.708203933 + -4 = -10.708203933 r = -10.708203933 Simplifying r = -10.708203933

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.708203933, -10.708203933}

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