2x2-12x-54 = 0
Solve by factoring or using the quadratic equation formula or by completing the square:
(2x+6)(x-9) = 0
Therefore: x = -3 or x = 9
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To find the original number when given the prime factors, we have to work backwards. First, we simplify into 2 squared times 3 squared. (2x2) x (3x3) Then we expand the brackets. 4 x 9 = 54 Therefore 54 is the number, with 2x2 and 3x3 as the prime factors.
-9x + 2y = -69 So 2y = 9x - 69 The other equation can be written as 6x - 4y = 54 or 6x - 2*2y = 54 Substituting for 2y gives 6x - 2*(9x - 69) = 54 6x - 18x + 138 = 54 12x = 84 x = 7 and then 2y = 9x - 69 = 9*7 - 69 = 63-69 = -6 so that y = -3
54
To find out what number multiplied by 18 equals 54, you can set up an equation: 18x = 54. To solve for x, divide both sides by 18: x = 54 / 18. Simplifying the division gives x = 3. Therefore, 18 times 3 equals 54.
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