SOLUTION: Solve each equation and to check for extraneous solutions [√(2x^2 + 5x + 6)]=x

Question 1185300: Solve each equation and to check for extraneous solutions
[√(2x^2 + 5x + 6)]=x
Answer by Edwin McCravy(20054) (Show Source): You can put this solution on YOUR website!




We square both sides:



When we square a square root we take away the square and the square root:



Subtract x² from both sides:





Use the zero factor principle. Set each factor equal to 0:

x+3 = 0;   x+2 = 0
  x = -3;    x = -2

We substitute those in the original equation to see if both are
solutions to the original equations, or extraneous:

Substituting x = -3











That's false.  So -3 is an extraneous solution, so we discard it.

Substituting -2











That's false.  So -2 is also an extraneous solution, so we discard it.

The equation has no solution.

Note: The symbol "√(" always means the POSITIVE square root. To indicate
the negative square root, there must be a negative sign before it "-√(".

Edwin

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