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When completing the square, we first divide the whole equation by the x^2 component. In this case, the x^2 component is 1 so nothing changes. We now apply the method to convert to square form: we reduce the ...

When any curve crosses the x-axis, the y-coordinate is 0 at that point. Hence, our answers will have y=0. So we want to solve x^2+6x+5=0. From before, we have that x^2+6x+5=0 can be rewritten as (x+5)(x+1)=0...

To start, notice that we have x^2 in our equation. This means that our answer is of the form (x )(x ). We now look for integers that give 5 when multiplied together. The only way we can do this is with the n...

Bacterial resistance to antibiotics is an example of natural selection. In a population of bacteria there may be some individuals that are not affected by the antibiotic. This may be due to random changes or...

Crude oil is separated into fractions in a process called fraction distillation. The crude oil mixture is separated in a distillation column. The column is hot at the bottom and cool at the top. Fractional d...