r^2+16r-45=0

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Solution for r^2+16r-45=0 equation:


Simplifying
r2 + 16r + -45 = 0

Reorder the terms:
-45 + 16r + r2 = 0

Solving
-45 + 16r + r2 = 0

Solving for variable 'r'.

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 16r + 45 + r2 = 0 + 45

Reorder the terms:
-45 + 45 + 16r + r2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 16r + r2 = 0 + 45
16r + r2 = 0 + 45

Combine like terms: 0 + 45 = 45
16r + r2 = 45

The r term is 16r.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16r + 64 + r2 = 45 + 64

Reorder the terms:
64 + 16r + r2 = 45 + 64

Combine like terms: 45 + 64 = 109
64 + 16r + r2 = 109

Factor a perfect square on the left side:
(r + 8)(r + 8) = 109

Calculate the square root of the right side: 10.440306509

Break this problem into two subproblems by setting 
(r + 8) equal to 10.440306509 and -10.440306509.

Subproblem 1

r + 8 = 10.440306509 Simplifying r + 8 = 10.440306509 Reorder the terms: 8 + r = 10.440306509 Solving 8 + r = 10.440306509 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = 10.440306509 + -8 Combine like terms: 8 + -8 = 0 0 + r = 10.440306509 + -8 r = 10.440306509 + -8 Combine like terms: 10.440306509 + -8 = 2.440306509 r = 2.440306509 Simplifying r = 2.440306509

Subproblem 2

r + 8 = -10.440306509 Simplifying r + 8 = -10.440306509 Reorder the terms: 8 + r = -10.440306509 Solving 8 + r = -10.440306509 Solving for variable 'r'. Move all terms containing r to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + r = -10.440306509 + -8 Combine like terms: 8 + -8 = 0 0 + r = -10.440306509 + -8 r = -10.440306509 + -8 Combine like terms: -10.440306509 + -8 = -18.440306509 r = -18.440306509 Simplifying r = -18.440306509

Solution

The solution to the problem is based on the solutions from the subproblems. r = {2.440306509, -18.440306509}

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