Question

Express the following in completed square form:

y = (2x)^2 + 14x - 11

Please show the work because I do not understand it.

Answer 1

recall that a^2+2ab+b^2 = (a+b)^2
(2x)^2 + 14x - 11
4x^2 + 14x - 11
4(x^2 + 7/2) - 11
4(x^2 + 7/2 + (7/4)^2) - 11 - 4(49/16)
4(x + 7/4)^2 - 44/4 - 49/4
4(x + 7/4)^2 - 93/4

Answer 2

The answer in the book says:

y = 2 (x+7/2)^2 -71/2

Answer 3

(2x)^2 + 14x - 11
checking if x=1, value is 4+14-11=7
checking book answer, if x=1, 2(9/2)^2-71/2=10
checking oobleck's answer: if x=1, y=4(1+7/4)^2-93/4=121/4-93/4=128/4=7
book answer is wrong.