How do you do this problem ?

Question

Solve the equation.
x2 + 3x - 40 = 0

x = -5, x = 8
x = -5, x = - 8
x = 5, x = - 8
x = -40, x = 0

Answer 1

You are going to have to factor it first.
First step is what number multiplied together will give you 40.
possible numbers are
40 *1 = 40
20 * 2 = 40
5 * 8 = 40
next look at the signs: you will notice +3x and - 40 that tells you one of the numbers you are mutliplying is negative because of the - 40 a + and a - multipled together gives you a negative product right? Laws of signed numbers.

Now you look at 3x and see it is a + which means the larger of the two numbers will be positive and the smaller will be negative right? Again the Laws of signed numbers.
Now that you know that much next step is to analyze equation to see which two numbers multiplied together will give you -40 while at the same time when added together will give you a +3x
First step x = -5, x =8 will give you a - 40 when multipied together. but what about if they are added together?
(+8) + ( - 5) = +3 again the Laws of signed numbers:

second set of numbers: x= -5, x = -8 when multiplied together will give you a + 40 wrong sign so we discard them.

third set of numbers x = 5, x = -8 when multiplied together will give you a - 40 already so we add them together.
(+5) + ( - 8) = - 3 again wrong because it is negative not positive.

Fourth set x= -40, x = 0 is wrong because 40 * 0 = 0

First set is two numbers we need in order to factor the quation because (- 5) * ( +8) = - 40 and ( - 5 ) + ( +8) = 3

Now we can factor the equation in factored terms:
Remember this about factoring a quadratic equation, what you are doing is finding out what numbers multiplied together with give you that equation. In essence that equation is the product of two numbers multiplied together and what you are doing when you factor is you are finding those two numbers.

Next step x^2 is the easy one since x*x = x^2 right?
now we factor: break the equation down into the two numbers multiplied together that will give us x^2 + 3x - 40 = 0

We know we have to multiply x and x together to get x^2
and we have to multiply - 5 and 8 together to get - 40
next step we write it out.
first we plug in x * x
next we plug in - 5 and + 8
which gives us:
x -5 and x + 8
Now since x^2 + 3x - 40 = 0 is the product of x - 5 and x + 8 we know we are going to have to multiply them together:
so our answer is:
(x - 5) * (x + 8) = 0
With laws of quadratic equations that gives you:
x = - 5 and x = +8
now to check our answer:
x - 5
x +8
-------
x^2 - 5x
........+8x - 40
-------------------
x^2 + 3x - 40

Answer checks out.

Hope that helps it takes a lot of practice to get good at factoring. and you have to be fimiliar with your signed numbers and your prime numbers along with numbers that are factors of other numbers. such as 5, and 8 being factors of 40.