Completing the Square
Completing the Squaree.g. (i ) x 2  6 x  7  0
Completing the Squaree.g. (i ) x 2  6 x  7  0               x2  6x  7    move the constant
Completing the Squaree.g. (i ) x 2  6 x  7  0               x2  6x  7        move the constant        x 2  6 x  32 ...
Completing the Squaree.g. (i ) x 2  6 x  7  0               x2  6x  7        move the constant        x 2  6 x  32 ...
Completing the Squaree.g. (i ) x 2  6 x  7  0               x2  6x  7        move the constant        x 2  6 x  32 ...
Completing the Squaree.g. (i ) x 2  6 x  7  0               x2  6x  7         move the constant        x 2  6 x  32...
(ii ) ax 2  bx  c  0
(ii ) ax 2  bx  c  0            b     c      x2  x   0            a    a
(ii ) ax 2  bx  c  0            b     c      x2  x   0            a     a                b       c           x  x...
(ii ) ax 2  bx  c  0            b      c      x2  x   0            a      a                 b      c           x  x...
(ii ) ax 2  bx  c  0            b      c      x2  x   0            a      a                 b      c           x  x...
(ii ) ax 2  bx  c  0            b      c      x2  x   0            a      a                 b      c           x  x...
(ii ) ax 2  bx  c  0            b      c      x2  x   0            a      a                 b      c           x  x...
(iii ) x 2  6 x  6  0
(iii ) x 2  6 x  6  0      x  3       0                2
(iii ) x 2  6 x  6  0      x  3 3  0              2
(iii ) x 2  6 x  6  0       x  3 3  0               2 x  3  3  x  3  3   0
(iii ) x 2  6 x  6  0       x  3 3  0               2 x  3  3  x  3  3   0x  3  3 or x  3  3
(iii ) x 2  6 x  6  0       x  3 3  0               2 x  3  3  x  3  3   0x  3  3 or x  3  3     Exer...
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11X1 T01 09 completing the square (2011)

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11X1 T01 09 completing the square (2011)

  1. 1. Completing the Square
  2. 2. Completing the Squaree.g. (i ) x 2  6 x  7  0
  3. 3. Completing the Squaree.g. (i ) x 2  6 x  7  0 x2  6x  7 move the constant
  4. 4. Completing the Squaree.g. (i ) x 2  6 x  7  0 x2  6x  7 move the constant x 2  6 x  32  7  32 add half the coefficient of ‘x’ squared
  5. 5. Completing the Squaree.g. (i ) x 2  6 x  7  0 x2  6x  7 move the constant x 2  6 x  32  7  32 add half the coefficient of ‘x’ squared x 2  6 x  9  16  x  3  16 2 factorise to a perfect square
  6. 6. Completing the Squaree.g. (i ) x 2  6 x  7  0 x2  6x  7 move the constant x 2  6 x  32  7  32 add half the coefficient of ‘x’ squared x 2  6 x  9  16  x  3  16 2 factorise to a perfect square x  3  4
  7. 7. Completing the Squaree.g. (i ) x 2  6 x  7  0 x2  6x  7 move the constant x 2  6 x  32  7  32 add half the coefficient of ‘x’ squared x 2  6 x  9  16  x  3  16 2 factorise to a perfect square x  3  4 x  3  4 x  7 or x  1
  8. 8. (ii ) ax 2  bx  c  0
  9. 9. (ii ) ax 2  bx  c  0 b c x2  x   0 a a
  10. 10. (ii ) ax 2  bx  c  0 b c x2  x   0 a a b c x  x 2 a a
  11. 11. (ii ) ax 2  bx  c  0 b c x2  x   0 a a b c x  x 2 a a 2 2x2  x         b b c b     a  2a  a  2a 
  12. 12. (ii ) ax 2  bx  c  0 b c x2  x   0 a a b c x  x 2 a a 2 2x2  x         b b c b     a  2a  a  2a  2 x b  c  b 2    2a  a 4a 2 b 2  4ac  4a 2
  13. 13. (ii ) ax 2  bx  c  0 b c x2  x   0 a a b c x  x 2 a a 2 2x2  x         b b c b     a  2a  a  2a  2 x b  c  b 2    2a  a 4a 2 b 2  4ac  4a 2 b b 2  4ac x  2a 2a
  14. 14. (ii ) ax 2  bx  c  0 b c x2  x   0 a a b c x  x 2 a a 2 2x2  x         b b c b     a  2a  a  2a  2 x b  c  b 2    2a  a 4a 2 b 2  4ac  4a 2 b b 2  4ac x  2a 2a b  b 2  4ac x 2a
  15. 15. (iii ) x 2  6 x  6  0
  16. 16. (iii ) x 2  6 x  6  0  x  3 0 2
  17. 17. (iii ) x 2  6 x  6  0  x  3 3  0 2
  18. 18. (iii ) x 2  6 x  6  0  x  3 3  0 2 x  3  3  x  3  3   0
  19. 19. (iii ) x 2  6 x  6  0  x  3 3  0 2 x  3  3  x  3  3   0x  3  3 or x  3  3
  20. 20. (iii ) x 2  6 x  6  0  x  3 3  0 2 x  3  3  x  3  3   0x  3  3 or x  3  3 Exercise 1I; 1adh, 2ch, 3adg, 4bdfh, 5bdf, 6adg, 7bc, 8*

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