SOLUTION: How do I find all the real-number roots of the equation and give an exact expression for the root and also a calculator approximation rounded to three decimal places. {{{ log(

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: How do I find all the real-number roots of the equation and give an exact expression for the root and also a calculator approximation rounded to three decimal places. {{{ log(       Log On


   



Question 747365: How do I find all the real-number roots of the equation and give an exact expression for the root and also a calculator approximation rounded to three decimal places.
+log%28+2%2C+x%29+%2B+log%28+2%2C+%28x+%2B+6%29%29+=+0+

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Note that +0+=+log%282%2C1%29+
+log%28+2%2C+x%29+%2B+log%28+2%2C+%28x+%2B+6%29%29+=+0+
+log%28+2%2C+x%29+%2B+log%28+2%2C+%28x+%2B+6%29%29+=+log%28+2%2C1+%29+
+log%28+2%2C+x%2A%28+x%2B6+%29+%29+=+log%28+2%2C1+%29+
+log%28+2%2C+x%5E2+%2B+6x+%29+=+log%28+2%2C1+%29+
+x%5E2+%2B+6x+=+1+
Complete the square
+x%5E2+%2B+6x+%2B+%286%2F2%29%5E2+=+1+%2B+%286%2F2%29%5E2+
+x%5E2+%2B+6x+%2B+9+=+10+
+%28+x+%2B+3+%29%5E2+=+10+
+x+%2B+3+=+sqrt%2810%29+
+x+=+-3+%2B+sqrt%2810%29+
and
+x+=+-3+-+sqrt%2810%29+