Section Two - Algebra Part 3

Section Two - Algebra Part 3

1. Rearranging Formula

   • Method
     • Get rid of any square root signs by squaring both sides
       • Get rid of any fractions
         • Multiply out any brackets
           • Collect all subject terms on one side and all the non-subject terms on the other
             • Reduce it to the form 'AX = B'
               • Divide both sides by A to give 'X = ...'
                 • If you're left with 'X2 =...', square root both sides to get 'X = +-'

2. Factorising Quadratics

   • Putting it into 2 brackets
   • aX2 + bX +c = 0
   • Method when a = 1
     • Always rearrange into the standard format: x2 +bx + c =0
       • Write down the two brackets with the Xs in : (X )(X ) = 0
         • Find 2 numbers that multiply to give 'c' but also add/subtract to give 'b'
           • Fill in the +/- signs and make sure they work out properly
             • Expand the brackets to make sure they give the original equation and solve

3. Quadratic Formula

   • Get into the ax2 + bx +c = 0 form
     • Identify a,b and c
       • Put these values into the formula
         • Then check by putting the values into the original equation

4. Completing the Square

   • x2 + 12x - 5 = (x +6)2 - 41
   • rearrange the quadratic to the aX2 + bX +c = 0 form
     • Write out the initial bracket: (x + b/2)2
       • Multiply out the brackets and compare to the original
         • Add or subtract the adjusting number to make it match the original

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