Quadratics

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.

1) Rearrange the equation into the standard format.

X2+8x+5

2) Wrire the initial bracket as (x+b/2)2. Divide `b` by two, add x and square the whole thing.

(X+4)2X2+8x+5

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.