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Question 815698: [ The point (x,1) is 4 times the square root of 2 units from (2,3). Find x. ]
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! distance between two points:
d = sqrt( dx^2 + dy^2 )
where:
dx is the difference between the x-coordinates
dy is the difference between the y-coordinates
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d = sqrt( dx^2 + dy^2 )
4*sqrt(2) = sqrt( (x - 2)^2 + (1 - 3)^2 )
(4*sqrt(2))^2 = (x - 2)^2 + (1 - 3)^2
16*2 = (x - 2)^2 + (-2)^2
32 = xx - 4x + 4 + 4
xx - 4x - 24 = 0
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the above quadratic equation is in standard form, with a=1, b=-4, and c=-24
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to solve the quadratic equation, plug this:
1 -4 -24
into this: https://sooeet.com/math/quadratic-equation-solver.php
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the roots of the quadratic are:
x = 7.29150262
x = -3.29150262
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Answer:
both roots are valid values for x
(i.e. both roots answer the question as to what is the value of x.)
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