Question

(x + 6 )ao quadrado =25x -4

Answer 1

Resposta:

$(x+6)^{2} =25x-4\\(x+6)^{2} = x^{2} +12x+36=25x-4\\ x^{2} +12x+36 -25x+4=0\\ x^{2} -13x+40=0$

Usando Bhaskara:

$x = \frac{-b+ \sqrt{b^{2} -4ac}  }{2a} \\\\Ou\\\\x = \frac{-b- \sqrt{b^{2} -4ac}  }{2a}$

Temos que a = 1, b = - 13 e c = 40.

Substituindo os valores, obtemos:

$x = \frac{-(-13)+ \sqrt{(-13)^{2} -4(1)(40)}  }{2(1)} = \frac{13+\sqrt{169-160} }{2} = \frac{13+\sqrt{9} }{2} = \frac{13+3}{2} = \frac{16}{2} = 8\\\\ou\\x = \frac{-(-13)- \sqrt{(-13)^{2} -4(1)(40)}  }{2(1)} = \frac{13-\sqrt{169-160} }{2} = \frac{13-\sqrt{9} }{2} = \frac{13-3}{2} = \frac{10}{2} = 5$\\Ou\\x = \frac{-(-13)- \sqrt{(-13)^{2} -4(1)(40)}  }{2(1)} \\\\\\[/tex]

Portanto, x = 8 ou x = 5.