Question

resolva a equação (12+x).(4+x)=153

Answer 1

Equação do segundo grau

$\sf{(12 + x) \times (4 + x) = 153} \\ \\ \sf{48 + 12x + 4x + {x}^{2} = 153} \\ \\ \sf{48 + 16x + {x}^{2} = 153 } \\ \\ \sf{48 + 16x + {x}^{2} - 153 = 0} \\ \\ \sf{48 - 153 + 16x - {x}^{2} = 0 } \\ \\ \sf{ - 105 + 16x + {x}^{2} = 0} \\ \\ \sf{ {x}^{2} + 16x - 105 = 0 } \\ \\ \sf{x = \frac{ - 16\pm \sqrt{ {16}^{2} - 4 \times 1 \times (- 105) } }{2 \times 1} } \\ \\ \sf{x = \frac{ - 16\pm \sqrt{ {16}^{2} - 4 \times ( - 105)} }{2 \times 1} } \\ \\ \sf{x = \frac{ - 16\pm \sqrt{ {16}^{2} - 4 \times ( - 105)} }{2} } \\ \\ \sf{x = \frac{ - 16\pm \sqrt{256 - 4 \times ( - 105)} }{2} } \\ \\ \sf{x = \frac{ - 16\pm \sqrt{256 + 420} }{2} } \\ \\ \sf{x = \frac{ - 16\pm \sqrt{676} }{2} } \\ \\ \sf{x = \frac{ - 16\pm \sqrt{ {26}^{2} } }{2} } \\ \\ \sf{x = \frac{ - 16\pm26}{2} } \\ \\ \sf{ x_{1} = \frac{ - 16 + 26}{2} } \\ \\ \sf{ x_{2} = \frac{ - 16 - 26}{2} } \\ \\ \boxed{\sf{ x_{1} = 5}} \\ \\ \boxed{\sf{ x_{2} = - 21 }}$

Resposta: $\sf{ x_{1} = 5\:\: ; \:\: x_{2}= - 21 }$

Att: José Armando