Quandaries and Queries

My name is Jennifer a student in year 11. The following problems have me stuck and any help would be greatly appreciated seeing my text book is doing me no favours:

32a+1 - 283a + 9=0
52m - 5m=20

Thankyou for your time

Hi Jennifer,

Mny times solving an angebra problem is seeing a pattern. In your second problem 52m is the square of 5m, so the pattern I see is

(something squared) - (something) = 20 To use more conventional mathematical notation, let x = 5m, then the expression is x2 - x = 20 That is x2 - x - 20 = 0 which factors to give (x - 5)(x + 4) = 0 and hence x = 5 or x = -4.

Since x = 5m and 5m cannot be negative, the only solution is 5m = 5 and thus m = 1.

Can you now solve the first problem?

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