Question

pelo método de completar quadrados
d) x² + 15x/2 + 9= 0​

Answer 1

$x^2+\frac{15x}{2}+9=0]\\\\ \textsf{multiplicar os lados por 2}\\\\x^2\cdot \:2+\frac{15x}{2}\cdot \:2+9\cdot \:2=0\cdot \:2\\\\2x^2+15x+18=0\\\\ \textsf{\mathrm{Dividir\:ambos\:os\:lados\:por\:}2}\\\\\\\frac{2x^2+15x}{2}=\frac{-18}{2}\\\\x^2+\frac{15x}{2}=-9\\\\x^2+\frac{15x}{2}+\left(\frac{15}{4}\right)^2=-9+\left(\frac{15}{4}\right)^2\\\\x^2+\frac{15x}{2}+\left(\frac{15}{4}\right)^2=\frac{81}{16}\\\\\left(x+\frac{15}{4}\right)^2=\frac{81}{16}$

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$x+\frac{15}{4}=\frac{\sqrt{81}}{\sqrt{16}}\\\\x+\frac{15}{4}=\frac{\sqrt{81}}{4}\\\\x+\frac{15}{4}-\frac{15}{4}=\frac{9}{4}-\frac{15}{4}\\\\x=-\frac{3}{2}$

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$x+\frac{15}{4}=-\sqrt{\frac{81}{16}}\\\\x+\frac{15}{4}=-\frac{9}{4}\\\\x+\frac{15}{4}-\frac{15}{4}=-\frac{9}{4}-\frac{15}{4}\\x=-6$