SOLUTION: (2.11p + 3.42)2 = 9.58

Algebra ->  Square-cubic-other-roots -> SOLUTION: (2.11p + 3.42)2 = 9.58      Log On


   

Question 45778This question is from textbook Beginning & Intermediate Algebra
: (2.11p + 3.42)2 = 9.58 This question is from textbook Beginning & Intermediate Algebra

Found 2 solutions by tutorcecilia, atif.muhammad:
Answer by tutorcecilia(2152) About Me  (Show Source):
You can put this solution on YOUR website!
(2.11p + 3.42)2 = 9.58 [Distribute the 2]
4.22p + 6.84 = 9.58 [Solve for p]
4.22p + 6.84 - 6.84 = 9.58 -6.84
4.22p = 2.74
4.22p/4.22 = 2.74/4.22
p = 0.6493
.
Check by plugging p=0.76493 back into the original equation:
[(2.11)(0.6493) + 3.42)]2 = 9.58
9.58 = 9.58 [Checks out]

Answer by atif.muhammad(135) About Me  (Show Source):
You can put this solution on YOUR website!
(2.11p + 3.42)2 = 9.58
4.4521p^2 + 11.6964 + 14.4324p = 9.58
4.4521p^2 +2.1164 + 14.4324p = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ap%5E2%2Bbp%2Bc=0 (in our case 4.4521p%5E2%2B14.432p%2B2.1164+=+0) has the following solutons:

p%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=%2814.432%29%5E2-4%2A4.4521%2A2.1164=170.59292624.

Discriminant d=170.59292624 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-14.432%2B-sqrt%28+170.59292624+%29%29%2F2%5Ca.

p%5B1%5D+=+%28-%2814.432%29%2Bsqrt%28+170.59292624+%29%29%2F2%5C4.4521+=+-0.153958502490248
p%5B2%5D+=+%28-%2814.432%29-sqrt%28+170.59292624+%29%29%2F2%5C4.4521+=+-3.08765781340562

Quadratic expression 4.4521p%5E2%2B14.432p%2B2.1164 can be factored:

Again, the answer is: -0.153958502490248, -3.08765781340562. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4.4521%2Ax%5E2%2B14.432%2Ax%2B2.1164+%29