beenbad510
28.01.2020 •
Mathematics
59: 14
the diagram shows a vertical number line.
what is the position of point x?
0 -16
-12
12
Solved
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Ответ:
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.