Question 4

Question 1

Complete the square on

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Or, you could:

There's nothing more to do from here.

You are asked to complete the square on $\simplify{x^2+{b}x + {c}}$

The exponent of x is 2, so we halve it to get $\var{p}$.

Squaring this gives $\var{p^2}$.

We can write

\[\simplify{x^2+{b}x + {c}} = \simplify[all, !collectNumbers]{x^2+{b}x + {p^2} - {p^2} + {c}}\]

The first three terms are a perfect square, so we have

\[\simplify{x^2+{b}x + {c}} = \simplify[all,!collectNumbers]{(x+{p})^2 - {p^2} + {c}}\]

Leading to

\[\simplify{x^2+{b}x + {c}} = \simplify{(x+{p})^2 - {p^2} + {c}}\]

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