Question

1. (2x-7)^2-7(7-4x)= 9

Answer 1

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$\displaystye \bf \Big(2x-7 \Big)^2-7 \Big(7-4x \Big)=9\\\\ \Big(2x \Big)^2-2\cdot \:2x\cdot \:7-\Big(-7\cdot \:7-\left(-7\right)\cdot \:4x\Big)=9\\\\4x^2-28x+49-49+28x=9\\\\4x^2=9\\\\4x^2-9=0$

$\displaystyle \bf D=b^2-4ac=\Big(0\Big)^2-4\cdot 4 \cdot \Big(-9\Big)=144$

$\displaystyle \bf X_{1:2}=\frac{-b\pm\sqrt D}{2a} =\frac{-0\pm\sqrt {144}}{2 \cdot 4} =\frac{-0 \pm \sqrt {144}}{8} =\frac{-0 \pm12}{8}$

$\boxed { \Big \displaystyle \bf X_1=\frac{-0+12}{8} =\frac{12}{8} =\frac{3}{2} \\\\ }$

$\boxed{\Big \displaystyle \bf X_2=\frac{-0-12}{8} =-\frac{12}{8} =-\frac{3}{2}}}$