r^2-14r-45=0

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Solution for r^2-14r-45=0 equation: 


Simplifying
r2 + -14r + -45 = 0

Reorder the terms:
-45 + -14r + r2 = 0

Solving
-45 + -14r + 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 + -14r + 45 + r2 = 0 + 45

Reorder the terms:
-45 + 45 + -14r + r2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + -14r + r2 = 0 + 45
-14r + r2 = 0 + 45

Combine like terms: 0 + 45 = 45
-14r + r2 = 45

The r term is -14r.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14r + 49 + r2 = 45 + 49

Reorder the terms:
49 + -14r + r2 = 45 + 49

Combine like terms: 45 + 49 = 94
49 + -14r + r2 = 94

Factor a perfect square on the left side:
(r + -7)(r + -7) = 94

Calculate the square root of the right side: 9.695359715

Break this problem into two subproblems by setting 
(r + -7) equal to 9.695359715 and -9.695359715.


Subproblem 1
r + -7 = 9.695359715

Simplifying
r + -7 = 9.695359715

Reorder the terms:
-7 + r = 9.695359715

Solving
-7 + r = 9.695359715

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + r = 9.695359715 + 7

Combine like terms: -7 + 7 = 0
0 + r = 9.695359715 + 7
r = 9.695359715 + 7

Combine like terms: 9.695359715 + 7 = 16.695359715
r = 16.695359715

Simplifying
r = 16.695359715


Subproblem 2
r + -7 = -9.695359715

Simplifying
r + -7 = -9.695359715

Reorder the terms:
-7 + r = -9.695359715

Solving
-7 + r = -9.695359715

Solving for variable 'r'.

Move all terms containing r to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + r = -9.695359715 + 7

Combine like terms: -7 + 7 = 0
0 + r = -9.695359715 + 7
r = -9.695359715 + 7

Combine like terms: -9.695359715 + 7 = -2.695359715
r = -2.695359715

Simplifying
r = -2.695359715


Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {16.695359715, -2.695359715}

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