Right we've got an equation to solve, but
in this format we can't do much with it, so
we need to put it into the standard format.
So expand these brackets first of all.
2x times x, that's 2 x-squared.
2x times 4, is + 8x... equals 1.
Now we want to get it equal to 0, so take
1 from both sides, and then it'll be in our
standard format.
OK, now it says give you solutions to 3 significant
figures, so that means our solutions aren't
whole numbers.
So, we're going to have to use the formula.
Now I'm sure you'll know the formula off by
heart.
But if you do forget it, or if you want to
check it, it will be at the front of the exam
paper… but you should be so familiar with
it that you know it off by heart.
So… [reads out formula].
And now we can write down the values of a,
b and c for our particular equation.
'a' is 2, 'b' is 8, 'c' is -1.
So now put it into the formula.
So x equals minus b (-8)... plus or minus
the square root of... b squared (so that's
8 squared), minus 4 a c... so that's 4 times
'a' which is 2, times 'c' which is -1 (here's
where we have to be careful with the minus
numbers) ... over 2a, so that's 2 times 2.
Right, -8 plus or minus the square root of...
8 squared (that's 64)... minus 4 times 2 (that's
8), times -1 (so that's -8).
So we've got minus minus 8, so it's actually
plus 8... over 2 times 2 which is 4.
OK, so that is actually -8 plus or minus root
72.
Over 4.
OK, now we can't do much with that, now we
need to use our calculator.
So here we go.
This is where you need to know where all the
buttons are.
Now here they've simplified the surd form,
but we want a decimal, so if I press that
change button on this calculator it'll give
me a decimal.
So, we want to write down a few decimal places,
0.121320... that'll do.
And now we need to do it when it's minus root
72...
So 
it's 'or' -4.121320...
So they're our two solutions but we need to
have it as 3 significant figures... so here's
it's going to be [counting one two three...]
x = 0.121 (we don't need to round up there)
or [counting one two three...] so -4.12.
OK, and they're our two solutions.
4 marks for that.
You'll get 1 mark if you rearrange the equation
into that form... and 1 mark if you put the
values correctly into the formula, and another
mark if you get this far, so if you get the
correct surd form.
So a bit of everything with this question
really – a bit of algebra, bit of formula,
bit of calculator, bit of rounding, bit of
everything.
