9514 1404 393
Answer:
x = 2
Explanation:
Taking antilogs, the equation becomes ...
x(x +3) = 10
x^2 +3x +2.25 = 12.25 . . . . add (3/2)² to complete the square
(x +1.5)² = 3.5² . . . . write as squares
x = -1.5 +3.5 . . . . . . take the positive square root*
x = 2
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* The negative square root gives an extraneous solution (x=-5).
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I find that using a graphing calculator with the original equation avoids extraneous solutions. Here we transform the equation to the form f(x) = 0, so the x-intercept is the value of x we seek.