x^2 - 4x - 5 = 0 How do you solve this equation by factoring?

Question

Please break it down into simple form for me so that I can understand and be able to do the rest of my assignment.

Answer 1

You know the first term is x^2 so you can write:
(x )(x )
You know that the second term is -4x:
If factors are of the form (x+A)(x+B) then Ax+Bx = -4x
You also know that the last term is -5, so A*B=-5

Just find the values of A and B that satisfy these equations:
Ax+Bx = -4x
A*B = -5

A = -5 and B = 1

NOW that we have the factors
(x-5)(x+1)=0
To get 0 either section of the left hand side can be 0, so solve both cases:
CASE 1:
x-5 =0
x = 5
CASE 2:
x+1=0
x=-1

ANSWER x=5 or x=-1

Answer 2

the answer for this particular problem is

(x-5)(x+1)=0

so you know x-5 or x+1 has to = 0 (thats the zero product property)

x-5=0 or x+1=0
x=5 or x=-1

so the final answer is x=5, -1


that might not help you be able to figure out the rest of them, though. it helps me to think of it like this. each problem has 3 parts: an x^2 coefficient, an x coefficient, and a constant. in this case those three parts were 1, -4, and -5 (dont forget the negative signs!). practicing is really the only way to get better at factoring, because its all about guessing and checking. each time youre going to factor it into 2 binomials with x +/- something. go ahead and write that down:

(x+ )(x+ )

(the pluses might change into minuses at the end if you have to fill in the blank with a negative number)

for the two blanks, you need numbers that when multiplied together will equal the constant (-5 in this case) and when added will give you the x coefficient (-4 in this case).

see how the answer fits that description?
-5*1=-5
-5+1=-4

but what if you dont think of that right away? start by listing the factors of your constant, to see what possible combinations you could have. for -5 its easy, your only choices are 1 and -5 or -5 and 1. now test your options to see which of them will meet the other requirement, which is that they add up to -4.

-1+5=4 (so thats not the answer)
-5+1=-4 (so that is it!)

this becomes a little harder for a number like 12, because you have more factor choices (1 and 12, -1 and -12, 3 and 4, -3 and -4, 2 and 6, -2 and -6) but thats the general approach.

now that you know the two numbers, just plug them in like this:

(x+-5)(x+1)=0
simplify . . . (x-5)(x+1)=0
and finish solving like i did at the top.


if the negatives mess you up, keep these patterns in mind-
1. if the constant and the x coefficient are both positive, then you have two pos. numbers
2. if the constant is pos and the x coeff. is neg, then you have two neg. numbers
3. if the constant is neg, then you have one pos. and one neg. number. (if the x coeff. is pos, then the higher number value is the pos. one) (if the x coeff is neg, then the lower number value is the neg. one)


if the x^2 coeff. isnt 1, then it makes things a little more tricky but i dont know how well i can explain that here so ill skip that for now. i hope this helps you get the hang of factoring problems! good luck :)

Answer 3

First you have to put the first variable in 2 parenthesis:

(x )(x )=0

The reason this is so is because x times x is x^2.

The next step is to determine whether the sign will be addition or subtraction. Since the last variable is -5, the signs inside the parenthesis will be a + sign and a - sign, as shown below:

(x+ )(x- )=0

The reason this is so is because a negative times a positive is a negative.

The next step is to put the numbers in. You want to find out what whole numbers can be multiplyed together to make 5. The only combonation is 1 and 5. The next part is to figure out what order the numbers are put inside the parenthesis. In this problem it is as follows:

(x+1)(x-5)=0

You can check this method by using FOIL or First, Outer, Inner, Last. The First thing to multiply are the 2 x's which gives us x^2. When you multiply the Outer and Inner variables, it gives you 1x -5x, which when put into an equation makes -4x. Does it look familiar? It should, it's the middle variable. Then you multiply the Last's which happen to be 1 and -5. This gives you the last variable -5.

After you have put the numbers in the correct order [(x+1)(x-5)],
you set both groups of parenthesis to 0, like so:

(x+1)=0 (x-5)=0

This means that x is either -1 or 5. If x is a measurement, then it has to be a positive number.

Sorry for explaining every little detail. This kind of problem is hard to explain when you are assuming that the askee doesn't know anything.

Answer 4

Just find two numbers that multiply to make -5, (the last part of the equation) and then put them into the components (x + n1)(x + n2). So n1 and n2 should be 1 and -5 since 1 x -5 = -5. There is no other options here.

Verify the product of these two expressions equals the equations

(x-5)(x+1)
= x * x + -5 * x + 1 * x + -5 * 1
= x^2 - 5x + x - 5
= x^2 - 4x - 4

If either one of the expressions is 0, the whole thing will be zero, therefore, x = -1 OR x = 5

Verify by plugging the values into your equation and making sure they evaluate to zero.

Answer 5

you basically do foil backward...

So you would start by looking at the x^2 and the -5. and by using those two numbers you come up with a way to break both of them down into smaller number that when added equal a -4x.

the factors of x^2 and -5

x^2 only factors into X and X

while -5 has factors of... 1 -5, -1 5 (these factors come from numbers that can mulitply to get the original number in this case it is -5)

outcome should be either (x-5)(x+1)=0 or (x+1)(x-5)=0

hope this was helpful!

Answer 6

x2 – 4x – 5 = 0 (x - 5) (x + a million) = 0 So x = +5 or x = -a million For the quadratice equation: a = a million, b = -4, c = -5 Sqrt b^2 - 4ac = sqrt (16 - (4 * a million * -5)) = sqrt (16 - (-20)) = sqrt (36) = +6 or -6 The quadratic equation is then: [- (-4) +/- 6 ]/ 2 = 2 +/- 3 = +5 or -a million

Answer 7

(x - 5)(x + 1) = 0
x = 5 or -1

www.quickmath.com will factor it for you

Just find factors of 5, which is 5 and 1, now you either have -5 and 1 or 5 and -1. Since -5 + 1 = -4, those are your values to use in (x + a)(x + b) whereas a = -5 and b = 1.

If you can't factor it, then you have use the completing the square method. To check to see if it can be factored just use the site i gave you.

Answer 8

well the way my teacher taught me is look at the last #. its negative, so find 2 numbers that multiply to 5 and subtract to 4. if the last #'s positive, 2 numbers that multiply to 5 and add to 4. but its negative. so 5 and 1. since the last #'s negative, one # will be positive and one will be negative. and since the middle #'s negative, the bigger # will be negative. so set it up: (x )(x ). then add the numbers: (x 1)(x 5). then add the signs (x+1)(x-5)=0 (u dont need =0 usually). to check, multiply through, and if u get the beginning equation, ur right. so x*x=x^2, x*-5=-5x, 1*x=x, and 1*-5=-5. so add them. x^2+-5x+x+-5. so x^2-4x-5. so x is -1 or 5 to make one of the 2 equal to 0. so (-1+1)(-1-5)=(0)(-6)=0, or (5+1)(5-5)=(6)(0)=0.

Answer 9

You have to use the numbers that divide evenly into 5 (ie 1, -1, 5, and -5) to find what you use in factorizing. Since -5 + 1 = -4, then

x^2 - 4x - 5 = 0
So (x - 5)(x + 1) = 0
So x = 5 or x = -1

Answer 10

x^2 - 4x - 5 = 0
Factor:
(x+1)(x-5) = 0
Now either x+1 =0 and x= -1,
or x-5 = 0 and x = 5