What substitution should be used to rewrite 6(x + 5)2 + 5(x + 5) – 4 = 0 as a quadratic equation?
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Step-by-step explanation:
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x = -4 and x = -19/3
Step-by-step explanation:
6(x+5)^{2} + 5(x+5) - 4 = 0
Solution : Let x+5= k ------------> (a)
6k^2 + 5k -4 = 0
6k^2 + 8k - 3k - 4=0
2k(3k+4) - 1(3k+4) = 0
(2k-1) (3k+4) = 0
Therefore k = 1 , -4/3
Substitute in (a)
(i) x+5 = 1 ; x = -4
(ii) x+5 = -4/3
x= (-4/3)-5
x= (-4-15)/3 = -19/3
Therefore x= -4 , -19/3
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