Solve for r:
-10 = r^2-10 r+12
-10 = r^2-10 r+12 is equivalent to r^2-10 r+12 = -10:
r^2-10 r+12 = -10
Subtract 12 from both sides:
r^2-10 r = -22
Add 25 to both sides:
r^2-10 r+25 = 3
Write the left hand side as a square:
(r-5)^2 = 3
Take the square root of both sides:
r-5 = sqrt(3) or r-5 = -sqrt(3)
Add 5 to both sides:
r = 5+sqrt(3) or r-5 = -sqrt(3)
Add 5 to both sides:
Answer: | r = 5+sqrt(3) or r = 5-sqrt(3)
Solve for r:
-10 = r^2-10 r+12
-10 = r^2-10 r+12 is equivalent to r^2-10 r+12 = -10:
r^2-10 r+12 = -10
Add 10 to both sides:
r^2-10 r+22 = 0
r = (10±sqrt((-10)^2-4×22))/2 = (10±sqrt(100-88))/2 = (10±sqrt(12))/2:
r = (10+sqrt(12))/2 or r = (10-sqrt(12))/2
sqrt(12) = sqrt(4×3) = sqrt(2^2×3) = 2sqrt(3):
r = (10+2 sqrt(3))/2 or r = (10-2 sqrt(3))/2
Factor 2 from 10+2 sqrt(3) giving 2 (5+sqrt(3)):
r = 2 (5+sqrt(3))/2 or r = (10-2 sqrt(3))/(2)
(2 (5+sqrt(3)))/2 = 5+sqrt(3):
r = 5+sqrt(3) or r = (10-2 sqrt(3))/(2)
Factor 2 from 10-2 sqrt(3) giving 2 (5-sqrt(3)):
r = 5+sqrt(3) or r = 2 (5-sqrt(3))/2
(2 (5-sqrt(3)))/2 = 5-sqrt(3):
Answer: | r = 5+sqrt(3) or r = 5-sqrt(3)
