SOLUTION: Find the real solution of the equation sqrt 32-4x=x

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Question 376158: Find the real solution of the equation sqrt 32-4x=x
Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28+32++-+4x+%29+=+x
square both sides. Note that squaring means that you can get solutions that are not suitable, in this case if you get a solution of a negative x:
32-4x+=+x%5E2+
Solved by pluggable solver: EXPLAIN simplification of an expression
Your Result:


YOUR ANSWER


  • This is an equation! Solutions: x=-8,x=4.
  • Graphical form: Equation 32-4x=x%5E2 was fully solved.
  • Text form: 32-4x=x^2 simplifies to 0=0
  • Cartoon (animation) form: simplify_cartoon%28+32-4x=x%5E2+%29
    For tutors: simplify_cartoon( 32-4x=x^2 )
  • If you have a website, here's a link to this solution.

DETAILED EXPLANATION

Look at highlight_red%28+32+%29-4%2Ax=x%5E2.
Moved 32 to the right of expression
It becomes -4%2Ax%2Bhighlight_green%28+32+%29=x%5E2.
Look at -4%2Ax%2B32=highlight_red%28+x%5E2+%29.
Moved these terms to the left highlight_green%28+-x%5E2+%29
It becomes -4%2Ax%2B32-highlight_green%28+x%5E2+%29=0.
Look at -4%2Ax%2Bhighlight_red%28+32+%29-x%5E2=0.
Moved 32 to the right of expression
It becomes -4%2Ax-x%5E2%2Bhighlight_green%28+32+%29=0.
Look at highlight_red%28+-4%2Ax-x%5E2%2B32+%29=0.
Equation highlight_red%28+-4%2Ax-x%5E2%2B32=0+%29 is a quadratic equation: -x^2-4*x+32 =0, and has solutions -8,4
It becomes highlight_green%28+0+%29=0.
Result: 0=0
This is an equation! Solutions: x=-8,x=4.

Universal Simplifier and Solver


Done!


x = -8 is a WRONG root, because square root cannot be negative. So your answer is x=4.