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Let t as y² + 5y .
[tex] {y}^{2} + 5y = t[/tex]
Rewrite the equation :
[tex]t - \frac{36}{t} = 0 \\ [/tex]
Multiply sides by t
[tex]t \times (t - \frac{36}{t} ) = t \times 0 \\ [/tex]
[tex] {t}^{2} - 36 = 0[/tex]
Add sides 36
[tex] {t}^{2} - 36 + 36 = 0 + 36[/tex]
[tex] {t}^{2} = 36[/tex]
[tex]t = ± \: 6[/tex]
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So :
[tex] {y}^{2} + 5y = 6[/tex]
Subtract sides 6
[tex] {y}^{2} + 5y - 6 = 6 - 6[/tex]
[tex] {y}^{2} + 5y - 6 = 0[/tex]
[tex](y + 6)(y - 1) = 0[/tex]
[tex]y = - 6 \: \: or \: \: y = 1[/tex]
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[tex] {y}^{2} +5y = - 6[/tex]
[tex]No \: \: solution[/tex]
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Thus (( y = 1 )) and (( y = - 6 )) are the roots of the equation .
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