Question

Expresse em números decimais as reais as raízes da equação x (4x-1)=3 (x+1).

Answer 1

Olá, boa noite!

Feliz ano ano!

$x(4x-1)=3(x+1)\\4x^2-x=3x+3\\4x^2-x-3x-3=0\\4x^2-4x-3=0\\\\Coeficientes:\;a=4,\;b=-4\;e\;c=-3\\\\\Delta=b^2-4ac\\\Delta=(-4)^2-4\cdot4\cdot(-3)\\\Delta=16+48\\\Delta=64\\\\x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\x=\dfrac{-(-4)\pm\sqrt{64}}{2\cdot4}\\\\x=\dfrac{4\pm8}{8}\\\\x_1=\dfrac{4+8}{8}=\dfrac{12}{8}=\boxed{\dfrac{3}{2}=1,5}\\\\x_2=\dfrac{4-8}{8}=-\dfrac{4}{8}=\boxed{-\dfrac{1}{2}=-0,5}$




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