Solve x2 − 12x + 5 = 0 using the completing-the-square method. x = six plus or minus the square root of five x = negative six plus or minus the square root of five x = six plus or minus the square root of thirty one x = negative six plus or minus the square root of thirty one

we are given

we have to solve it by completing square method

step-1: Move 5 on right side

step-2: Break middle term

step-3: Add 6^2 both sides

step-3: Solve for x

we wil get two values

First value is

add both sides 6

Second value is

add both sides 6

so, solutions are

.............Answer

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for