SOLUTION: can you please help me solve this question:(((One eighth of the square root of 7 less than a number is 2. what is the number? )))

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Question 176370This question is from textbook algebra structure and method
: can you please help me solve this question:(((One eighth of the square root of 7 less than a number is 2. what is the number? ))) This question is from textbook algebra structure and method

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
x-%281%2F8%29sqrt%287%29=2
:
8x-sqrt%287%29=16multiplied all terms by 8
:
sqrt%287%29=8x-16adjusted terms so sqrt was isolated
:
sqrt%287%29%5E2=%288x-16%29%5E2squared both sides
:
7=64x%5E2-128x-128x%2B256multiplied terms
:
64x%5E2-256x%2B249=0combined terms and place all terms on one side
:
2.33 is the answer
:
1.67 is and extraneous root
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 64x%5E2%2B-256x%2B249+=+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=%28-256%29%5E2-4%2A64%2A249=1792.

Discriminant d=1792 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--256%2B-sqrt%28+1792+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-256%29%2Bsqrt%28+1792+%29%29%2F2%5C64+=+2.33071891388307
x%5B2%5D+=+%28-%28-256%29-sqrt%28+1792+%29%29%2F2%5C64+=+1.66928108611693

Quadratic expression 64x%5E2%2B-256x%2B249 can be factored:
64x%5E2%2B-256x%2B249+=+%28x-2.33071891388307%29%2A%28x-1.66928108611693%29
Again, the answer is: 2.33071891388307, 1.66928108611693. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+64%2Ax%5E2%2B-256%2Ax%2B249+%29