This text is missing some spaces, please add them: Valuesofx1,x2andcanbedeterminedwhichsatisfythefirstorderconditions.
Values of x1, x2 and can be determined which satisfy the first order conditions.
input question: Fix spacing: Thus,allparticipantsremainsthefascinatingideaoftheexperience.

output answer: Thus, all participants remains the fascinating idea of the experience.
Problem: Therewasquitesomeactivitythenexthoursonall5floors,reallyagoodstartofthefestival.
What's a sentence that uses these characters?
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There was quite some activity the next hours on all 5 floors, really a good start of the festival.
Add spaces: Atthesametimeweareinpossessionofgreatexperienceinhandlingandmixingoflow-viscositytoveryviscousproducts,andalsodosing/mixingandin-housetransportofpowderproductsforthefoodindustry,thepharmaceuticalandcosmeticindustry,andthechemical/technicalindustry.

Answer: At the same time we are in possession of great experience in handling and mixing of low-viscosity to very viscous products, and also dosing/mixing and in-house transport of powder products for the food industry, the pharmaceutical and cosmetic industry, and the chemical/technical industry.
Thefreeversionisnotupdatedasoftenastheproversion,andsincetimeisessentialinthearmsracewiththevirusmakers,updatesareveryimportant.

The free version is not updated as often as the pro version, and since time is essential in the arms race with the virus makers, updates are very important.
Add spaces: Infinancialtrading,instructionsandstepsmustbesimpletounderstand.

Answer:
In financial trading, instructions and steps must be simple to understand.