The product of two consecutive even number is 168. find the numbers

even numbers can be represented as 2n where n is an integer

consecutive even integers are 2 apart (2,4,6,8, etc)

so 2 consecutive even integers can be represeted as 2n and 2n+1

their product is 168, so

(2n)(2n+2)=168

expand/distribute

4n²+4n=168

factor out a 4

4(n²+n)=168

divide both sides by 4

n²+n=42

solve by completing the square

take 1/2 of the linear coefient and square it

the linear coeffient is 1 so 1/2 of 1 is 1/2, and (1/2)^2=1/4

add 1/4 to both sides

n²+n+1/4=42+1/4

factor perfect square trinomial

square root both sides

subract 1/2 from both sides

n=-0.5+6.5 or -0.5-6.5

n=6 or -7

if n=6, then 2n=12 and 2n+2=12+2=14

if n=-7, then 2n=-14 and 2n+2=-14+2=-12

so the 2 numbers are 12 and 14 or -12 and -14 (the problem didn't specify the sign of the numbers)

answer: what equations are there

step-by-step explanation:

5x+40

5(x + 8)

7x - 49

7(x - 7)

18x + 9

9(2x + 1)

15x - 10

5(3x - 2)

step-by-step explanation:

for number one all you have to do is factor 5 out of 5x + 40

for number 2 factor 7 out of 7x - 49

for number three factor 9 out of 18x + 9

for number four factor 5 out of 15x - 10