If 110x = 1020four, find the value of x.
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110x = 1020four
Change both bases to base 10 and find x.
1 x x2 + 1 x x1 + 0 x x0 = 1 x 43 + 0 x 42 + 2 x 41 + 0 x 40
x2 + x = 64 + 8
x2 + x = 72
x2 + x - 72= 0
The co-efficient of x is 1 hence split x into two numbers when multiplied will produce -72 and when added will produce 1
The numbers are 9 and -8
x2 + 9x - 8x - 72 = 0
x(x + 9) - 8(x + 9) = 0
(x + 9)(x - 8) = 0
If x + 9 = 0, x = -9
If x - 8 = 0, x = 8
Since bases are positive, x = 8.