Question

a^2+14a-51=0

Answer 1

a=3,-17

Answer 2

how to work it out

Answer 3

Do you know how to factor the left side?

Answer 4

like add 51 on both sides

Answer 5

No, you need to write the left side as the product of two quantities.

Answer 6

how

Answer 7

Since you have three terms, and one of them has a squared variable, follow these factoring rules:
1. First, try to factor a common factor out.
In this case, 1, 14 and -51 have no common factor so there's no common factor to take out.
2. Set up two sets of parentheses:
(a )(a )

Answer 8

Now you are looking for two numbers that when you multiply together you get -51, and when you add together you get 14.

Answer 9

Can you think of two such numbers?

Answer 10

17 and 3

Answer 11

Right, but since the product needs to be NEGATIVE 51, and the sum +14, you need +17 and -3. -17 and + 3 will not work because although their product is -51, their sum is -14, not +14.

Answer 12

Ok, so now you know the numbers are -3 and 17. Just place them inside the two parentheses like this:
(a - 3)(x + 17) = 0

Answer 13

Now the left side is factored.

Answer 14

The next step is the following:
You have a product whose result is zero. How can you get a zero as the result of the multiplication of two numbers?

Answer 15

The product that is zero is (a + 17) times (a - 3).
The only way that product can be zero is if one of the factors is zero. Now you need to see what values of a make these factors zero, so you write:
a - 3 = 0 or a + 17 = 0
Solve these simple equations and you get:
a = 3 or a = -17

Answer 16

so i can do this on every problem to get dis answer

Answer 17

This is the method for problems of the type:
x^2 + ax + c = 0
where a and b are numbers, and x is the variable.
For example:
x^2 - x - 2 = 0
y^2 - y - 12 = 0

Answer 18

ok x^2+6x+8=0 answer is -2,-4

Answer 19

(x + 4)(x + 2) = 0
x + 4 = 0 or x + 2 = 0
x = -4 or x = -2
You are correct.

Answer 20

ok i got it thanks

Answer 21

wlcm