SOLUTION: Sorry not sure what kind of algebra it is. the question is from nov03 edexcel gcse paper, and tells us the area of a trapezium is 36cm^2 show that x^2-x-56=56, which i got to

Question 77064: Sorry not sure what kind of algebra it is.
the question is from nov03 edexcel gcse paper, and tells us the area of a trapezium is 36cm^2
show that x^2-x-56=56, which i got to be,
1/2(a+b)h
=1/2(x+2+x+6)x-5
1/2(2x+8)x-5=36
x+4 multiplied by x-5
36 =x^2-20+4x-5
therefore x^2-x-56=0
is that right?
and then it asks you to solve the equation x^2-x-56=0
i've got so far
x^2-x=56
x^2=56+x
but i never know what to do next? please help!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)

In order to factor , first we need to ask ourselves: What two numbers multiply to -56 and add to -1? Lets find out by listing all of the possible factors of -56

Factors:

1,2,4,7,8,14,28,56,

-1,-2,-4,-7,-8,-14,-28,-56,List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to -56.

(-1)*(56)=-56

(-2)*(28)=-56

(-4)*(14)=-56

(-7)*(8)=-56

Now which of these pairs add to -1? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -1

||||||||

First Number	\|	Second Number	\|	Sum
1	\|	-56	\|	1+(-56)=-55
2	\|	-28	\|	2+(-28)=-26
4	\|	-14	\|	4+(-14)=-10
7	\|	-8	\|	7+(-8)=-1
-1	\|	56	\|	(-1)+56=55
-2	\|	28	\|	(-2)+28=26
-4	\|	14	\|	(-4)+14=10
-7	\|	8	\|	(-7)+8=1

We can see from the table that 7 and -8 add to -1.So the two numbers that multiply to -56 and add to -1 are: 7 and -8 Now we substitute these numbers into a and b of the general equation of a product of linear factors which is: substitute a=7 and b=-8 So the equation becomes: (x+7)(x-8) Notice that if we foil (x+7)(x-8) we get the quadratic again

Now set each factor equal to zero

So our answer is:
or
Since a negative answer doesn't work, the answer is
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