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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1.3 You subtract 3.2 from 1.9 ; which gives you 1.3
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Mordancy.