r^2+18r+16=45

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Solution for r^2+18r+16=45 equation:


Simplifying
r2 + 18r + 16 = 45

Reorder the terms:
16 + 18r + r2 = 45

Solving
16 + 18r + r2 = 45

Solving for variable 'r'.

Reorder the terms:
16 + -45 + 18r + r2 = 45 + -45

Combine like terms: 16 + -45 = -29
-29 + 18r + r2 = 45 + -45

Combine like terms: 45 + -45 = 0
-29 + 18r + r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '29' to each side of the equation.
-29 + 18r + 29 + r2 = 0 + 29

Reorder the terms:
-29 + 29 + 18r + r2 = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 18r + r2 = 0 + 29
18r + r2 = 0 + 29

Combine like terms: 0 + 29 = 29
18r + r2 = 29

The r term is 18r.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18r + 81 + r2 = 29 + 81

Reorder the terms:
81 + 18r + r2 = 29 + 81

Combine like terms: 29 + 81 = 110
81 + 18r + r2 = 110

Factor a perfect square on the left side:
(r + 9)(r + 9) = 110

Calculate the square root of the right side: 10.488088482

Break this problem into two subproblems by setting 
(r + 9) equal to 10.488088482 and -10.488088482.

Subproblem 1

r + 9 = 10.488088482 Simplifying r + 9 = 10.488088482 Reorder the terms: 9 + r = 10.488088482 Solving 9 + r = 10.488088482 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + r = 10.488088482 + -9 Combine like terms: 9 + -9 = 0 0 + r = 10.488088482 + -9 r = 10.488088482 + -9 Combine like terms: 10.488088482 + -9 = 1.488088482 r = 1.488088482 Simplifying r = 1.488088482

Subproblem 2

r + 9 = -10.488088482 Simplifying r + 9 = -10.488088482 Reorder the terms: 9 + r = -10.488088482 Solving 9 + r = -10.488088482 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + r = -10.488088482 + -9 Combine like terms: 9 + -9 = 0 0 + r = -10.488088482 + -9 r = -10.488088482 + -9 Combine like terms: -10.488088482 + -9 = -19.488088482 r = -19.488088482 Simplifying r = -19.488088482

Solution

The solution to the problem is based on the solutions from the subproblems. r = {1.488088482, -19.488088482}

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