ax² = Quadratic Term         bx = Linear Term         c = Constant

Factoring -  Move all terms to one side of the equation and have zero on the

other.   Factor the side with the terms and set all factors equal to zero.

x² + 6 = 5x            Move the 5x to the left side of the equation and put it in

                               middle, (change sign of 5x)  so there is decreasing exponents of x.

x² - 5x + 6 = 0       Factor the left side of the equation.

(x - 3)(x - 2) = 0    Set each factor equal to zero and solve.

x - 3 = 0      x - 2 = 0

   x = 3         x = 2     {2 ,3}     Answer

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4x² - 12x + 9 = 0               Factor the left side of the equation.

(2x - 3)² = 0                       Set each factor equal to zero.

2x - 3 = 0        2x - 3 = 0

2x = 3       2x = 3               Only use one 3/2 in your

x = 3/2       x = 3/2            answer, as an element of a set

         {3/2}   Answer        is never used more than once).

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3r(4r - 7) - 2 = 4                Multiply using the distributive property and move

                                            all terms to the left side of the equation.

12r² - 21r - 2 - 4 = 0         Combine like terms.

12r² - 21r - 6 = 0               Factor the left side of the equation.

3(4r² - 7r - 2) = 0             

3(4r + 1)(r - 2) = 0            Set all factors equal to zero.

3 = 0                  4r + 1 = 0    r - 2 = 0

no answer           4r = -1         r = 2

                                r = -¼         r = 2                  {-1/4 , 2}           Answer

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x³ + 2x² - 15x = 0             Factor the left side of the equation.

x(x² + 2x - 15) = 0

x(x + 5)(x - 3) = 0            Set all factors equal to zero.

x = 0        x + 5 = 0       x - 3 = 0

x = 0           x = -5              x = 3             {-5, 0, 3} Answer -  When all the terms of the left

 side of the equation contain the variable you are solving for, one answer is 0.  If

the degree of the equation is 3, then there are 3 answers.

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 Square Root Property - These equations will have only two terms,  after all terms

are combined. (ax² + c = 0) There will be only a quadratic term(ax²)and a

constant term [c]. Combine all like terms and move the constant term to

the opposite side of the equation and then take the square root of both

sides of the equation.

x² - 5 = 0                                    Move the 5 to the right side of the equation.

x² = 5                                          Take the square root of both sides of the equation.

REMEMBER TO PUT A ± IN FRONT OF THE ANSWER.

X = ± 5             {± 5}                Answer

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2x² - 162 = 0                              Move the 162 to the right side of the equation.

2x² = 162                                    Divide both sides of the equation by 2.

x² = 81                                        Take the square root of both sides of the equation.

x = ± 9                 {± 9}               Answer

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(x  -  4)²  =  225                         Take the square root of both sides.

  x  -  4    =    ±15                        Remember to put a ± in front of the 15.

  x  =    4   ± 15                            Move the 4 to the right side of the equation.

  4  +  15,     4  -  15                    Two answers

     19              -11      {-11, 19}     Answer

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 25x²  -  40x  +  16  =  75          Factor the left side of the equation.  It must factor

      (5x  -  4)²  =  75                    into a binomial squared.

        5x  -  4    =   ± Ö 75             Take the square root of both sides. 

         5x  =  4   ± Ö 75                 Move the four to the right side of the equation.

         x  =   (4  ± Ö 75) / 5          Divide both sides of the equation by 5.

                                                     Your answer is a fraction with 4  ± Ö75 in the

                                                      numerator and 5 in the denominator.

       Ö75    means square root of 75.