Y = - 16x² + 121x + 107

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