How do you solve #7p^2+16=2151#?

Question

Abigail Allen · Accepted Answer

#+-17.5#

First rearrange the equation to have all like terms on one side and unlike terms on the other:

#7p^2 = 2135#

Divide by #7# to get #p# on its own and then square root it.

#p^2 = 305# #sqrt(p^2)= +-sqrt(305)#

#p =+-sqrt(305)#

#= +-17.4642492#

#= +-17.5 # (to 3 sf)

Eva Adamson · Answer

See a solution process below:

First, subtract #color(red)(16)# from each side of the equation to isolate the #p# term while keeping the equation balanced: #7p^2 + 16 - color(red)(16) = 2151 - color(red)(16)# #7p^2 + 0 = 2135# #7p^2 = 2135# Next, divide each side of the equation by #color(red)(7)# to isolate #p^2# while keeping the equation balanced: #(7p^2)/color(red)(7) = 2135/color(red)(7)# #(color(red)(cancel(color(black)(7)))p^2)/cancel(color(red)(7)) = 305# #p^2 = 305# Now, take the square root of each side of the equation to solve for #p# while keeping the equation balanced. Remember, the square root of a number produces both a positive and negative result: #sqrt(p^2) = +-sqrt(305)# #p = +-17.464# rounded to the nearest thousandth.

Eli Assouline · Answer

undefined To solve the equation 7p^2 + 16 = 2151, you would follow these steps:

1. Subtract 16 from both sides to isolate the term with the variable:
   7p^2 = 2135

2. Divide both sides by 7 to solve for p^2:
   p^2 = 305

3. Take the square root of both sides to find the value of p:
   p = ±√305, which is approximately ±17.464

So, the solutions for p are p = 17.464 or p = -17.464.