Solve each quadratic equation by completing the square. 6. x2 + 2x = 8 7. x2 - 6x = 16 8. x2 - 18x = 19 9. x2 + 3x = 3 10. x2 + 7x = 8

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These questions have asked us to solve by completing the square.
How do we? I have attached a picture, which will explain

6. x² + 2x = 8
→ b is the coefficient of x, which is 2
→ We take half of 2 and square it. Then, we add it to either side

x² + 2x 
x² + 2x + 1 = 8 + 1
( x + 1 )( x + 1 ) = 9
( x + 1 )² = 9

x + 1 = + 3 or x + 1 = - 3
    x = 2     or     x = - 4

7. x² - 6x = 16

→ We do the same thing we did in the previous question

x² - 6x +  
x² - 6x + 9 = 16 + 9
(x - 3)² = 25

x - 3 = + 5 or x - 3 = - 5
   x = 8      or       x = - 2

8. x² - 18x = 19

x² - 18x +
x² - 18x + 81 = 19 + 81
( x - 9 )( x - 9 ) = 100
( x - 9 )² = 100

x - 9 = + 10 or x - 9 = -10
   x = 19      or      x = - 1

9. x² + 3x = 3

x² + 3x + 




 
x +   = + or x +
x =  or x =

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