6p2-42=72 The 6p is squared

Question

6p is squared.  I know the answer is 4,3 could you help me under stand how to work the problem out. Thank you

Answer 1

6p^2 - 42 = 72

 

Add 42 to both sides:

 

6p^2 = 42 + 72 = 114

 

Divide by 6 both sides:

 

p^2 = 19

 

Take square root of both sides:

 

|p| = √(19)

 

p = ±√(19)

Answer 2

Hi Roseland,

 

I want to try and answer your question here. Just to make sure the question is...

 

6(p)² - 42 = 72 solving for p.

 

So, there are many ways to solve this problem. The first method is to subtract 72 to both sides of the equation. 

 

6(p)² - 42 - 72 = 0 --> This leads to --> 6(p)² -114 = 0 --> Now you want to factor 6 from both terms (the 6(p)² term and the -114 term) --> This gives us...

 

6(p² -19) = 0 --> divide by 6 to the whole equation --> 6(p² -19)/6 = 0/6 --> 6(p² -19)/6 = 0/6 --> this gives us...

 

(p)² - 19 = 0 --> add 19 to both sides of the equation --> (p)² -19+19=0+19 --> (p)² = 19 --> take the square root of both sides of the equation to obtain the value of p.

 

p=(19)^1/2 --> p = 4.3588 

 

I hope this helped. Let me know if you have any questions about this solution.

Answer 3

Hi Roseland;

6p²-42=72

Let's subtract 72 from both sides...

6p²-42-72=72-72

6p²-114=0

Let's factor-out the 6...

6(p²-19)=0

The parenthetical equation must equal zero.  Therefore...

p²-19=0

(p+√19)(p-√19)=0

Let's FOIL...

FIRST...(p)(p)=p²

OUTER...(p)(-√19)=-p√19

INNER...(√19)(p)=p√19

LAST...(√19)(-√19)=-19

p²-(p√19)+(p√19)-19=0

p²-19=0

(p+√19)(p-√19)=0

Either or both parenthetical equations must equal zero...

p+√19=0

p=-√19

p-√19=0

p=√19

The square root of 19 is approximately 4.3.