SOLUTION: if a number is added to its square,the result is 42.find the number.

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Question 161996: if a number is added to its square,the result is 42.find the number.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let number be x....
if a number (x) is added to its square (x%5E2),the result is 42
x+%2B+x%5E2+=+42 or
x%5E2+%2B+x+-42+=+0.....use quadratic formula
Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve x%5E2%2Bx-42=0 ( notice a=1, b=1, and c=-42)





x+=+%28-1+%2B-+sqrt%28+%281%29%5E2-4%2A1%2A-42+%29%29%2F%282%2A1%29 Plug in a=1, b=1, and c=-42




x+=+%28-1+%2B-+sqrt%28+1-4%2A1%2A-42+%29%29%2F%282%2A1%29 Square 1 to get 1




x+=+%28-1+%2B-+sqrt%28+1%2B168+%29%29%2F%282%2A1%29 Multiply -4%2A-42%2A1 to get 168




x+=+%28-1+%2B-+sqrt%28+169+%29%29%2F%282%2A1%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-1+%2B-+13%29%2F%282%2A1%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-1+%2B-+13%29%2F2 Multiply 2 and 1 to get 2


So now the expression breaks down into two parts


x+=+%28-1+%2B+13%29%2F2 or x+=+%28-1+-+13%29%2F2


Lets look at the first part:


x=%28-1+%2B+13%29%2F2


x=12%2F2 Add the terms in the numerator

x=6 Divide


So one answer is

x=6




Now lets look at the second part:


x=%28-1+-+13%29%2F2


x=-14%2F2 Subtract the terms in the numerator

x=-7 Divide


So another answer is

x=-7


So our solutions are:

x=6 or x=-7





so, one answer is x=6 and another answer is x=-7
check:
x+%2B+x%5E2+=+42
6+%2B+6%5E2+=+42
6+%2B+36+=+42
42+=+42

x+%2B+x%5E2+=+42
-7+%2B+%28-7%29%5E2+=+42
-7+%2B+49=+42
42+=+42