From sea level, a submarine descends 30 feet per minute. Where is the submarine in relation to sea level 5 minutes after it starts descending?

  x = 4 ± (1/7)√721

Step-by-step explanation:

7x – 9 = 7x^2 – 49

-9 = 7x^2 -56x . . . . . . . . subtract 7x

-9 = 7(x^2 -8x) . . . . . . . . factor out leading coefficient

-9 +7(16) = 7(x^2 -8x +16) . . . . . add the square of (-8/2) inside parentheses

103 = 7(x -4)^2 . . . . . collect terms, write as a square

103/7 = (x -4)^2 . . . . divide by the leading coefficient

±√(103/7) = x -4 . . . . . take the square root

x = 4 ± (1/7)√721 . . . . add 4, rationalize the denominator

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You "complete the square" by making sure the constant in the quadratic is the square of half the x-term coefficient. If changes are made on one side of the equation, the same changes need to be made on the other side of the equation. Here, we added 7(16) to complete the square.