SOLUTION: a number exceeds its square root by 56. find the number

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Question 680947: a number exceeds its square root by 56. find the number
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
x+-+sqrt%28x%29+=+56
sqrt%28x%29+=+56-x
x+=+%2856-x%29%5E2
x+=+3136+-+112x+%2B+x%5E2
0+=+x%5E2+-+113x+%2B+3136
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-113x%2B3136+=+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=%28-113%29%5E2-4%2A1%2A3136=225.

Discriminant d=225 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--113%2B-sqrt%28+225+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-113%29%2Bsqrt%28+225+%29%29%2F2%5C1+=+64
x%5B2%5D+=+%28-%28-113%29-sqrt%28+225+%29%29%2F2%5C1+=+49

Quadratic expression 1x%5E2%2B-113x%2B3136 can be factored:
1x%5E2%2B-113x%2B3136+=+1%28x-64%29%2A%28x-49%29
Again, the answer is: 64, 49. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-113%2Ax%2B3136+%29

Possible solutions are x = 64 and x = 49
A square root can be negative, 64 and 8 work and so do 49 and -7
Both 56 and 49 are solutions