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(30) kind are called underline adfected quadratic equations. /underline

92. Simple quadratic equations are easily solved by the extraction of the square root. Thus if zz=25 it is evident, that formula Or in general if zz=a the formula. But if xx+6x=55, the value of a x is not as obvious.

93. The method in this and in the like cases is to compleat the square, which may always be done by adding to both sides of the equation, the square of half the known quantity of the second term. Thus in the equation xx+6x=55, the known quantity of the second term 6x is 6, half of which is 3, & the square of 3 is 9: Adding therefore 9 to both sides of the equation, we shall have xx+6x+9=55+9=64. Then extracting the square root of both sides, we have formula or x+3=8. Consequently