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solve : 4q² + 4q = 6 using two different methods

Two methods worth trying: Direct use of the quadratic formula on 4q² + 4q - 6 = 0. It's probably easier to divide everything by 4 first, giving q² + q - 3/2 = 0. The final answer can't be written as an exact decimal number so leave it in "closed form" - that is, instead of, say, writing 1.4142... for the square root of two, just write sqrt(2). A second method that works would be the method of "completing the square". You should be able to find this in the textbook, but here note that : (q+1/2)² = q² + q + 1/4 so that: q² + q = (q+1/2)² - 1/4. Then substitute this into your original equation. Both will give the same answer - because they're actually very closely related methods. Finally if you need a really different method there's always trial and error. Try q = 1. Then that would give the left hand side =8 but the right-hand side = 6, so 1 is too big, and so on.
05 September 2012
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