how can I simplify the last problem
26r-2=3r^2. We need to put this into standard form. The standard quadratic form is ax^2+bx+c=0, where x is the unknown and a, b and c are numbers. The unknown is r in this problem, rather than x, so let's put the equation into quadratic form: 3r^2-26r+2=0. How did I get this? Subtract 26r from each side: -2=3r^2-26r. Now, add 2 to each side: 0=3r^2-26r+2, which is the same as 3r^2-26r+2=0. (There's no mystery here. The equals sign shows us that we have equality of quantity. If, for example, an apple cost 30 cents or pennies, then 30 cents will buy an apple, so we can say apple=30 or 30=apple.)
This equation doesn't factorise, so we need the formula to solve it: r=(26+sqrt(26^2-4*3*2))/6 (this is the quadratic formula x=(-b+sqrt(b^2-4ac))/2a. All I've done is put b=-26, a=3 and c=2 into the formula. The plus-or-minus sign (+) means there are two answers, one using plus and the other using minus.) So r=(26+sqrt(676-24))/6=(26+sqrt(652))/6=8.589 or 0.0776. Because b=-26, -b=26: that's why the minus has disappeared.
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