Solving By Factoring
7p^2-50p=-7
Please show work for I could learn.
we know that 7*7 = 49 and 49+1 = 50 so we know what to do
7 p^2 - 50 p + 7 = 0
(7 p - 1) ( p - 7) = 0
The ticket the officer handed mom indicated she was speeding in a 45 mph construction zone in the amount of $215. Just how fast was mom traveling when the officer clocked her speeding?
Please show work!
To solve the equation 7p^2 - 50p = -7 using factoring, follow these steps:
Step 1: Rearrange the equation to bring all terms to one side.
7p^2 - 50p + 7 = 0
Step 2: Factor the quadratic expression on the left side of the equation.
To factorize it, we need to find two numbers whose product is 7*7 = 49 (the product of the coefficient of p^2 and the constant term) and whose sum is -50 (the coefficient of p). These numbers are -49 and -1.
7p^2 - 49p - p + 7 = 0
(7p(p - 7) - 1(p - 7)) = 0
Step 3: Notice that the terms (p - 7) are common to both terms. Factor it out.
(7p - 1)(p - 7) = 0
Step 4: Set each factor equal to zero and solve for p separately.
7p - 1 = 0 or p - 7 = 0
Solve for p in the first equation:
7p - 1 = 0
7p = 1
p = 1/7
Solve for p in the second equation:
p - 7 = 0
p = 7
Step 5: The solutions to the equation 7p^2 - 50p = -7 are p = 1/7 and p = 7.
So, the two values of p that satisfy the equation are p = 1/7 and p = 7.