Problema Solution
I think of a number x. If i square it and add it to the number i first thought of the total is 42. Find the number i first thought of...
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Answer provided by our tutors
The number that we need to find is x.
x^2 + x = 42 (the number i thought squared + the original number = 42)
x^2 + x - 42 = 0 (quadratic equations)
Using the formula for solving quadratic equations we have the solutions
x1 = (-1 + ((1^2)-(4*1*(-42))^0.5)/2*1 = (-1 + 169^0.5) /2 = (-1 + 13) / 2 = 12 /2 = 6
x2 = (-1 - ((1^2)-(4*1*(-42))^0.5)/2*1 = (-1 - 170^0.5) /2 = (-1 - 13) / 2 = - 14 /2 = -7
There are 2 solutions 6 and -7.
Indeed 6^2 + 6 = 42 and (-7)^2 - 7 = 42.