1) Rearrange into the standard format.
2) Write out the initial double brackets, x`s in both and possibly a number of x`s in one.
3) Find a pair of numbers that: Multiply to give c, and total to b.
4) Fill in the +/- signs to ensure it all works. To check, expend the brackets.
5) Solve the equation by making each bracket equal zero.
Completing the Square
1) Rearrange the equation into the standard format.
2) Wrire the initial bracket as (x+b/2)2. Divide `b` by two, add x and square the whole thing.
3) Multiply out the brackets and compare to the original question.
(X+4)2 = X2+8x+16 - Original equation had (+5).
4) Add or subtract the adjusting number to complete the square.
(X+4)2-11 = X2+8x+16-11 - ...So you need to take 11 to match.
=X2+8x+5 - Matches original now. So answer is: (X+4)2 - 11
1) Put it into standard format.
2) Decide what a, b and c are.
3) Substitute these values into the formula.
Whenever you get a minus value alarm bells should ring.
4) Type into calculator and get positive and negitive answer.
Check answer by substituting back into the equations angain.
Remember these things:
It is `2a` on the bottom of the fraction.
If I get a negitive number in the square root, im wrong. no negative roots at GCSE level.