Cassidy R.

# Which equation implies which? (for each)

This problem illustrates the logic involved in solving a quadratic equation by completing the square. (This particular equation can also be factored, but it's been chosen so as to keep the arithmetic simple.)

Enter (without the quotation marks) "==>" if the left equation implies the right, "<==" if the right equation implies the left, "<==>" if either equation implies the other, and "><" if neither equation implies the other.

x^2 + 2x - 8 = 0 __________ x^2 + 2x + 1 = 9. (add 9 on both sides).

x^2 + 2x + 1 = 9 __________ (x + 1)^2 = 9. (Apply the binomial formula x^2 + 2ax + a^2 = (x + a)^2, with a = 1, on both sides.)

x^2 + 2x + 1 = 9 __________ x + 1 = 3. (one possibility).

x^2 + 2x + 1 = 9 __________ x + 1 = -3. (the other possibility).

Thus the solutions of x^2 + 2x - 8 = 0 are x = -4 and x = 2.

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