I can't figure out how to factor out this quadratic exponential equation e^2x+7e^x-3=0 The answer in the book says it is -0.904 but I don't know how to figure out how to get the answer. Thank you
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Let $\displaystyle a = e^x$. Then $\displaystyle a^2 = e^{2x}$ $\displaystyle e^{2x} + 7 e^x - 3 = 0$ $\displaystyle a^2 + 7a - 3 = 0$ $\displaystyle a = \frac{-7\pm \sqrt{49 + 4.3}}{2}$ Then use $\displaystyle x = \ln a$.....
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