document.write( "Question 8083: Give the coordinates of a point on a coordinate grid that is a distance of the square root of 5 from point 1,3. Is there a formula to find the answer and how do you work out this problem?
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Algebra.Com's Answer #4448 by ichudov(507)\"\" \"About 
You can put this solution on YOUR website!
Yes, it is the pythagorean formula.\r
\n" ); document.write( "\n" ); document.write( "You are trying to find point (x, 0) where the y coordinate is zero, since it is on the X axis. \r
\n" ); document.write( "\n" ); document.write( "Points (1, 3), (1, 0), and (x, 0) form a right triangle. One side of it has length one. Another has length x-1. Sum of their squares should be 5:\r
\n" ); document.write( "\n" ); document.write( "\"1%5E2%2B%28x-1%29%5E2%29+=+5\"\r
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Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:

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  • This is an equation! Solutions: x=3,x=-1.
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  • Graphical form: Equation \"1%5E2%2B%28x-1%29%2A%28x-1%29=5\" was fully solved.
  • Text form: 1^2+(x-1)*(x-1)=5 simplifies to 0=0
  • Cartoon (animation) form: \"simplify_cartoon%28+1%5E2%2B%28x-1%29%2A%28x-1%29=5+%29\"
    For tutors: simplify_cartoon( 1^2+(x-1)*(x-1)=5 )
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  • If you have a website, here's a link to this solution.
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DETAILED EXPLANATION

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Look at \"highlight_red%28+1+%29%5Ehighlight_red%28+2+%29%2B%28x-1%29%2A%28x-1%29=5\".
Replace constants in factor: \"highlight_red%28+1+%29\",\"highlight_red%28+2+%29\" with \"highlight_green%28+1+%29\"
It becomes \"highlight_green%28+1+%29%2B%28x-1%29%2A%28x-1%29=5\".
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Look at \"1%2Bhighlight_red%28+%28x-1%29+%29%2Ahighlight_red%28+%28x-1%29+%29=5\".
Reduce similar several occurrences of \"highlight_red%28+%28x-1%29+%29\" to \"highlight_green%28+%28x-1%29%5E2+%29\"
It becomes \"1%2Bhighlight_green%28+%28x-1%29%5E2+%29=5\".
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Look at \"highlight_red%28+1+%29%2B%28x-1%29%5E2=5\".
Moved \"1\" to the right of expression
It becomes \"%28x-1%29%5E2%2Bhighlight_green%28+1+%29=5\".
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Look at \"%28x-1%29%5E2%2B1=highlight_red%28+5+%29\".
Moved these terms to the left \"highlight_green%28+-5+%29\"
It becomes \"%28x-1%29%5E2%2B1-highlight_green%28+5+%29=0\".
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Look at \"%28x-1%29%5E2%2Bhighlight_red%28+1+%29-highlight_red%28+5+%29=0\".
Added fractions or integers together
It becomes \"%28x-1%29%5E2%2Bhighlight_green%28+-4+%29=0\".
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Look at \"%28x-1%29%5E2%2Bhighlight_red%28+-4+%29=0\".
Removed extra sign in front of \"-4\"
It becomes \"%28x-1%29%5E2-highlight_green%28+4+%29=0\".
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Look at \"highlight_red%28+%28x-1%29%5E2-4+%29=0\".
Equation \"highlight_red%28+%28x-1%29%5E2-4=0+%29\" is a quadratic equation: x^2-2*x-3 =0, and has solutions 3,-1
It becomes \"highlight_green%28+0+%29=0\".
Result: \"0=0\"
\n" ); document.write( "This is an equation! Solutions: x=3,x=-1.

Universal Simplifier and Solver

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Done!
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