## zammett.damali 2 years ago a^2+14a-51=0

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1. Fox375

a=3,-17

2. zammett.damali

how to work it out

3. mathstudent55

Do you know how to factor the left side?

4. zammett.damali

like add 51 on both sides

5. mathstudent55

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

6. zammett.damali

how

7. mathstudent55

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 )

8. mathstudent55

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

9. mathstudent55

Can you think of two such numbers?

10. zammett.damali

17 and 3

11. mathstudent55

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.

12. mathstudent55

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

13. mathstudent55

Now the left side is factored.

14. mathstudent55

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?

15. mathstudent55

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

16. zammett.damali

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

17. mathstudent55

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

18. zammett.damali

19. mathstudent55

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

20. zammett.damali

ok i got it thanks

21. mathstudent55

wlcm