Mathematics, 06.07.2019 19:00 kukisbae

4= square root of (-6-2x) plus square root of (31-3x)

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Answer from: hatl

Step 1 :Isolate a square root on the left hand side :

     Original equation
     4 = √-6-2x+√31-3x

     Isolate
     -√-6-2x = -4+√31-3x

      Tidy up
     √-6-2x = 4-√31-3x

Step 2 :Eliminate the radical on the left hand side :

     Raise both sides to the second power
     (√-6-2x)2 = (4-√31-3x)2

     After squaring
     -6-2x = 31-3x+16-8√31-3x

Step 3 :Get remaining radical by itself :

     Current equation
     -6-2x = 31-3x+16-8√31-3x

     Isolate radical on the left hand side
     8√31-3x = 6+2x+31-3x+16

      Tidy up
     8√31-3x = 53-x

Step 4 :Eliminate the radical on the left hand side :

     Raise both sides to the second power
     (8√31-3x)2 = (53-x)2

     After squaring
     1984-192x = x2-106x+2809

Step 5 :Solve the quadratic equation :

     Rearranged equation
     x2  + 86x  + 825 = 0

     This equation has two rational roots:
       {x1, x2}={-11, -75}

Step 6 :Check that the first solution is correct :

     Original equation, root isolated, after tidy up
     √-6-2x = 4-√31-3x

     Plug in -11 for  x
      √-6-2•(-11) = 4-√31-3•(-11)

      Simplify
      √16 = -4
      Solution does not check
      4 ≠ -4

Step 7 :Check that the second solution is correct :

     Original equation, root isolated, after tidy up
     √-6-2x = 4-√31-3x

     Plug in -75 for  x
      √-6-2•(-75) = 4-√31-3•(-75)

      Simplify
      √144 = -12
      Solution does not check
      12 ≠ -12

Hopefully this helped You

Answer from: Quest

Definitely

Answer from: Quest

step-by-step explanation:

i used the pitagoras theoreme

Arectangular sheet of paper is folded diagonally from f to h . what is the length of side gh?<

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4= square root of (-6-2x) plus square root of (31-3x)...