SOLUTION: Yet another question. I keep doing something wrong with this 2(5x + 3)^2 = 38. Solve by extraction I keep coming up with answers that are not matching the back of the book. I try

Algebra ->  Square-cubic-other-roots -> SOLUTION: Yet another question. I keep doing something wrong with this 2(5x + 3)^2 = 38. Solve by extraction I keep coming up with answers that are not matching the back of the book. I try       Log On


   

Question 14007: Yet another question. I keep doing something wrong with this 2(5x + 3)^2 = 38. Solve by extraction
I keep coming up with answers that are not matching the back of the book. I try to distribute the two and then find the square root and work from there. I've tried 3 different ways. I'm not sure what I'm doing wrong. Please help
Answer by bam878s(77) About Me  (Show Source):
You can put this solution on YOUR website!
What you are doing wrong is distributing the two before taking the square. In equations certain operations have higher "authority" to perform before the others. Just remember the work PEMDAS. It means Parentheses Exponents Multiplication Division Addition Subtraction. These operations have "authority" going from highest to lowest, that is, Parentheses is the highest authority and Subtraction is the lowest.
Try this:
2%2A%285x%2B3%29%5E2=38
2(25x%5E2+%2B+30x+%2B+9) = 38.
NOW distribute the 2:
50x%5E2 + 60x + 9 = 38.
subtract 38 from both sides.
50x%5E2 + 60x - 29 = 0.
Now use the quadratic formula to solve for x.
x = %28-60%2B-sqrt%2860%5E2-4%2A50%2A%28-29%29%29%29%2F%282%2A50%29.
See if this works.