Answer:
r = 2/7 or -1
Explanation:
This equation can be factored more easily when put into standard form. Do that by adding 5r-2 to both sides.
7r² +5r -2 = 0
Now, you may notice that the middle coefficient is the sum of the other two. You can write it like that, then factor by grouping.
7r² +7r -2r -2 = 0 . . . . middle term split into two terms
7r(r +1) -2(r +1) = 0 . . . each pair of terms factored
(7r -2)(r +1) = 0 . . . . . . common factor factored out
This product will be zero only when one of the factors is zero. That is, the solutions to this equation will be the solutions to
7r -2 = 0 ⇒ r = 2/7
and
r +1 = 0 ⇒ r = -1
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If "solve this problem" means find values of the variable that satisfy the equation, then those values are ...
r = 2/7 or -1