Question

Resolva a equação x.(x-4)=-9 na fórmula de bhaskara

Answer 1

Dada a expressão:

$\mathsf{x\left(x-4\right)=-9}$

Resolução:

$\mathsf{x^2-4x=-9}\\\mathsf{x^2-4x+9=0}\\\\\\\mathsf{a=1\:,\:b=-4\:\:,\:c=9}\\\\\\\mathsf{\Delta =b^2-4ac}\\\mathsf{\Delta =\left(-4\right)^2-\left(4\cdot 1\cdot 9\right)}\\\mathsf{\Delta =16-36}\\\mathsf{\Delta =-20}$

$\mathsf{x=\dfrac{-b\pm \sqrt{\Delta }}{2a}}\\\\\\\mathsf{x=\dfrac{-\left(-4\right)\pm \sqrt{-20}}{2\cdot 1}}\\\\\\\mathsf{x=\dfrac{4\pm \sqrt{4\cdot 5\cdot \left(-1\right)}}{2}}\\\\\\\mathsf{x=\dfrac{4\pm 2\sqrt{5}i}{2}}\\\\\\\mathsf{x=2\pm \sqrt{5}i}\\\\\\\\\boxed{\mathsf{x_1=2+\sqrt{5}i\:\:\:\:\:\:\:\:e\:\:\:\:\:\:\:\:x_2=2-\sqrt{5}i}}\\\\\\\boxed{\boxed{\mathbf{Resposta:\:Nao\:existe\:solucao\:em\:\mathbb{R}}}}\: \: \checkmark$