Hi this ' True or False' question is in the 'GCSE Mathematics for AQA Higher Student Book' that we use at school
$30\frac{1}{4}$ must be added to $x^2 - 11x$ to make a perfect square.
I am sure that this is true because $x^2-11x$ in the form of $(x+p)^2+q$ would be $(x+5.5)^2$. And this expands to be $x^2-11x+34.35$, where the $34.25$ is added to the original expression.
However, the answer book gave me this:
False; $30\frac{1}{4}$ must be subtracted
which contradicts with everything I've explained above. And another logic I don't understand about their answer is that how can you factorize $x^2-11x-34.25$ into a perfect square if the '$34.25$' is a negative number (because you can't square root a negative no.?)
Please explain what has happened here, if it is me or the book who is wrong. And if my math was wrong then why. Thank you