Solve each equation by completing the square. If necessary, round to the nearest hundredth.

19. \( x^2 - 18x = 19 \)

20. \( 4a^2 + 8a - 20 = 0 \)

x 2 − 18 x = 19 x 2 − 2 x ⋅ 9 + 9 2 − 9 2 = 19 ( x − 9 ) 2 − 81 = 19 ( x − 9 ) 2 = 19 + 81 ( x − 9 ) 2 = 100 ⟺ x − 9 = ± 100 ​ x − 9 = − 10 ∨ x − 9 = 10 x = − 10 + 9 ∨ x = 10 + 9 x = − 1 ∨ x = 19
4 a 2 + 8 a − 20 = 0 / : 4 a 2 + 2 a − 5 = 0 a 2 + 2 a ⋅ 1 + 1 2 − 1 2 = 5 ( a + 1 ) 2 − 1 = 5 ( a + 1 ) 2 = 5 + 1 ( a + 1 ) 2 = 6 ⟺ a + 1 = ± 6 ​ a = − 6 ​ − 1 ∨ a = 6 ​ − 1 a ≈ − 3.45 ∨ a =≈ 1.45

Answered by Anonymous | 2024-06-10

To solve the equations, we completed the square for both equations. The solutions for x 2 − 18 x = 19 are x = 19 and x = − 1 , while for 4 a 2 + 8 a − 20 = 0 , the solutions are approximately a ≈ 1.45 and a ≈ − 3.45 .
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Answered by Anonymous | 2024-12-24