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Igoryamba
3 years ago
12

Consider the quadratic equation x2 − 6x = 16.

Mathematics
1 answer:
e-lub [12.9K]3 years ago
8 0

Answer:

  1. C) (x − 3)2 = 25
  2. C) Factor out 4 from 4x2 + 40x.

Step-by-step explanation:

1. Adding the square of half the x-coefficient to both sides of the equation will "complete the square." That square is 9, so the result on the right is 16+9 = 25. Only selection C matches.

___

2. To complete the square, you want to be able to put the quadratic into the form a(x -h)^2 = -k. For the purpose, it is most convenient to first factor "a" from the given quadratic. Then you can determine "-h" to be half the x-coefficient inside the parentheses.

Here, that looks like ...

  4(x² +10x) = 80 . . . . . . . . . . step 1: factor out 4

  4(x² +10x +25) = 180 . . . . . add 25 inside parentheses and the same number (4·25) on the right side of the equation

  4(x +5)² = 180 . . . . . . . . . . . written as a square

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