Resposta:
[tex]x _{1} = 5 + \frac{ \sqrt{97} }{2} \: \: \: \: \: \: \: \: x _{2} = 5 - \frac{ \sqrt{97} }{2} \\ [/tex]
Explicação passo-a-passo:
[tex] \blue{x(x - 2) = 3(x + 6)} \\x(x - 2) = 3(x + 6) \\x(x - 2) \\x(x - 2) = 3(x + 6) \\x {}^{2} - 2x = 3(x + 6) \\ 3(x + 6) \\ 3x + 18 \\ x {}^{2} - 2x = 3(x + 6) \\x {}^{2} - 2x = 3x + 18\\ x{}^{2} - 2x - 3x - 18 = 3x + 18 - 3x - 18 \\ x {}^{2} - 2x - 3x - 18 = 18 - 18 \\x {}^{2}2x - 3x - 18 = 0 \\x {}^{2} - 2x = 3x + 18\\x {}^{2} - 2x - 3x - 18 = 0 \\ - 2x - 3x \\( - 2 - 3)x \\ - 5 \\x {}^{2} - 2x - 3x - 18 = 0 \\x {}^{2} - 5 -18 = 0 \\x {}^{2} - 2 \times \frac{5}{2}x - 18 + ( \frac{5}{2}) {}^{2} - ( \frac{5}{2}) {}^{2} = 0 \\ \\(x - \frac{5}{2}) {}^{2} - 18 - ( \frac{5}{2}) {}^{2} = 0 \\ \\x {}^{2} - 5x - 18 = 0\\ \\ (x - \frac{5}{2}) {}^{2} - 18 - ( \frac{5}{2}) {}^{2} = 0 \\ \\ (x - \frac{5}{2} ) {}^{2} = 18 + ( \frac{5}{2}) {}^{2} \\ \\[/tex]
continuação
[tex](x - \frac{5}{2}) {}^{2} = 18 + \frac{5 {}^{2} }{2 {}^{2} } \\ \\5 {}^{2}\\ 5 \times 5\\25\\ (x - \frac{5}{2}) {}^{2} = 18 + \frac{5 {}^{2} }{2 {}^{2}}\\ \\ (x - \frac{5}{2}) {}^{2} = 18 + \frac{25}{2 {}^{2} }\\ \\2 {}^{2} \\ 2 \times 2 \\ 4 \\ \\ (x - \frac{5}{2}) {}^{2} = 18 + \frac{25}{2 {}^{2} } \\ \\ (x - \frac{5}{2}) {}^{2} = 18 + \frac{25}{4} \\ \\ (x - \frac{5}{2}) {}^{2} = \frac{97}{4} \\ \\ (x - \frac{5}{4}) {}^{2} = 18 + \frac{5 {}^{2} }{2 {}^{2} } \\ \\ (x - \frac{5}{2}) {}^{2} = \frac{97}{4} \\ \\x - \frac{5}{2} = + \frac{ \sqrt{97} }{4} \\ \\ x - \frac{5}{2} = + \frac{ \sqrt{97} }{2} \\ \\ x = + \frac{ \sqrt{97} }{2} + \frac{5}{2} \\ \\ x - \frac{5}{2} = + \frac{97}{4} \\ \\ x = + \frac{ \sqrt{97} }{2} + \frac{5}{2} \\ \\x = \frac{5}{2} + \frac{ \sqrt{97} }{2}\\ x = \frac{5}{2} - \frac{ \sqrt{97} }{2} \\ \\ x = \frac{5 + 27}{2} \\ x = \frac{5}{2} - \frac{ \sqrt{97} }{2} \\resposta \\ x_{1} = \frac{5 + \sqrt{97} }{2} \\ \\ x_{2} = \frac{5 - \sqrt{97} }{2} [/tex]
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Resposta:
[tex]x _{1} = 5 + \frac{ \sqrt{97} }{2} \: \: \: \: \: \: \: \: x _{2} = 5 - \frac{ \sqrt{97} }{2} \\ [/tex]
Explicação passo-a-passo:
[tex] \blue{x(x - 2) = 3(x + 6)} \\x(x - 2) = 3(x + 6) \\x(x - 2) \\x(x - 2) = 3(x + 6) \\x {}^{2} - 2x = 3(x + 6) \\ 3(x + 6) \\ 3x + 18 \\ x {}^{2} - 2x = 3(x + 6) \\x {}^{2} - 2x = 3x + 18\\ x{}^{2} - 2x - 3x - 18 = 3x + 18 - 3x - 18 \\ x {}^{2} - 2x - 3x - 18 = 18 - 18 \\x {}^{2}2x - 3x - 18 = 0 \\x {}^{2} - 2x = 3x + 18\\x {}^{2} - 2x - 3x - 18 = 0 \\ - 2x - 3x \\( - 2 - 3)x \\ - 5 \\x {}^{2} - 2x - 3x - 18 = 0 \\x {}^{2} - 5 -18 = 0 \\x {}^{2} - 2 \times \frac{5}{2}x - 18 + ( \frac{5}{2}) {}^{2} - ( \frac{5}{2}) {}^{2} = 0 \\ \\(x - \frac{5}{2}) {}^{2} - 18 - ( \frac{5}{2}) {}^{2} = 0 \\ \\x {}^{2} - 5x - 18 = 0\\ \\ (x - \frac{5}{2}) {}^{2} - 18 - ( \frac{5}{2}) {}^{2} = 0 \\ \\ (x - \frac{5}{2} ) {}^{2} = 18 + ( \frac{5}{2}) {}^{2} \\ \\[/tex]
continuação
[tex](x - \frac{5}{2}) {}^{2} = 18 + \frac{5 {}^{2} }{2 {}^{2} } \\ \\5 {}^{2}\\ 5 \times 5\\25\\ (x - \frac{5}{2}) {}^{2} = 18 + \frac{5 {}^{2} }{2 {}^{2}}\\ \\ (x - \frac{5}{2}) {}^{2} = 18 + \frac{25}{2 {}^{2} }\\ \\2 {}^{2} \\ 2 \times 2 \\ 4 \\ \\ (x - \frac{5}{2}) {}^{2} = 18 + \frac{25}{2 {}^{2} } \\ \\ (x - \frac{5}{2}) {}^{2} = 18 + \frac{25}{4} \\ \\ (x - \frac{5}{2}) {}^{2} = \frac{97}{4} \\ \\ (x - \frac{5}{4}) {}^{2} = 18 + \frac{5 {}^{2} }{2 {}^{2} } \\ \\ (x - \frac{5}{2}) {}^{2} = \frac{97}{4} \\ \\x - \frac{5}{2} = + \frac{ \sqrt{97} }{4} \\ \\ x - \frac{5}{2} = + \frac{ \sqrt{97} }{2} \\ \\ x = + \frac{ \sqrt{97} }{2} + \frac{5}{2} \\ \\ x - \frac{5}{2} = + \frac{97}{4} \\ \\ x = + \frac{ \sqrt{97} }{2} + \frac{5}{2} \\ \\x = \frac{5}{2} + \frac{ \sqrt{97} }{2}\\ x = \frac{5}{2} - \frac{ \sqrt{97} }{2} \\ \\ x = \frac{5 + 27}{2} \\ x = \frac{5}{2} - \frac{ \sqrt{97} }{2} \\resposta \\ x_{1} = \frac{5 + \sqrt{97} }{2} \\ \\ x_{2} = \frac{5 - \sqrt{97} }{2} [/tex]