SOLUTION: {{{log10(a)+log10(a+21)=2}}}

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Question 58099This question is from textbook Algebra 2
: log10%28a%29%2Blog10%28a%2B21%29=2 This question is from textbook Algebra 2

Answer by hayek(51) About Me  (Show Source):
You can put this solution on YOUR website!
Using: log10%28a%29%2Blog10%28b%29+=+log10%28a%2Ab%29
log10%28a%2A%28a%2B21%29%29=2
log10%28a%5E2%2B21a%29%29=2
10%5E2=%28a%5E2%2B21a%29
a%5E2%2B21a-100=0
Using quadratic formula, taking the positive solution (see below) a=4
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation a0%5E2%2Bb0%2Bc=0 (in our case 10%5E2%2B210%2B-100+=+0) has the following solutons:

0%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2821%29%5E2-4%2A1%2A-100=841.

Discriminant d=841 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-21%2B-sqrt%28+841+%29%29%2F2%5Ca.

0%5B1%5D+=+%28-%2821%29%2Bsqrt%28+841+%29%29%2F2%5C1+=+4
0%5B2%5D+=+%28-%2821%29-sqrt%28+841+%29%29%2F2%5C1+=+-25

Quadratic expression 10%5E2%2B210%2B-100 can be factored:
10%5E2%2B210%2B-100+=+1%280-4%29%2A%280--25%29
Again, the answer is: 4, -25. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B21%2Ax%2B-100+%29