SOLUTION: The sum of a number and 8, mulitipled by the sum of the number and 5 is equivalent to 19.

Algebra ->  Linear-equations -> SOLUTION: The sum of a number and 8, mulitipled by the sum of the number and 5 is equivalent to 19.      Log On


   

Question 1016156: The sum of a number and 8, mulitipled by the sum of the number and 5 is equivalent to 19.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
.
You did not ask a question.
Assuming you want to find the number.
.
x=the number
.
(x+8)(x+5)=19
x^2+13x+40=19
x^2+13x+21=0
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B13x%2B21+=+0) has the following solutons:

x%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=%2813%29%5E2-4%2A1%2A21=85.

Discriminant d=85 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-13%2B-sqrt%28+85+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2813%29%2Bsqrt%28+85+%29%29%2F2%5C1+=+-1.89022777135356
x%5B2%5D+=+%28-%2813%29-sqrt%28+85+%29%29%2F2%5C1+=+-11.1097722286464

Quadratic expression 1x%5E2%2B13x%2B21 can be factored:
1x%5E2%2B13x%2B21+=+1%28x--1.89022777135356%29%2A%28x--11.1097722286464%29
Again, the answer is: -1.89022777135356, -11.1097722286464. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B13%2Ax%2B21+%29

.
ANSWER: The number is -1.89 or -11.11.
.
CHECK:
.
For x=-1.89
(x+8)(x+5)=19
(-1.89+8)(-1.89+5)=19
(6.11)(3.11)=19
19=19
.
For -11.11
(-11.11+8)(-11.11+5)=19
(-3.11)(-6.11)=19
19=19
.