Answer:
x = 121/32 + sqrt(21489)/32 or x = 121/32 - sqrt(21489)/32
Step-by-step explanation:
Solve for x over the real numbers:
-16 x^2 + 121 x + 107 = 0
Divide both sides by -16:
x^2 - (121 x)/16 - 107/16 = 0
Add 107/16 to both sides:
x^2 - (121 x)/16 = 107/16
Add 14641/1024 to both sides:
x^2 - (121 x)/16 + 14641/1024 = 21489/1024
Write the left hand side as a square:
(x - 121/32)^2 = 21489/1024
Take the square root of both sides:
x - 121/32 = sqrt(21489)/32 or x - 121/32 = -sqrt(21489)/32
Add 121/32 to both sides:
x = 121/32 + sqrt(21489)/32 or x - 121/32 = -sqrt(21489)/32
Add 121/32 to both sides:
Answer: x = 121/32 + sqrt(21489)/32 or x = 121/32 - sqrt(21489)/32
