Complete the steps in solving the quadratic function 7x – 9 = 7x2 – 49x by completing the square.

–9 = 7x2 –
x

–9 +
= 7(x2 – 8x +
)

  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.

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to find the total number of combinations, multiply the quantity of each item by each other:

2 pairs of shoes x 3 pairs of shorts = 6 different combinations.