Question

Pelo amor de Deus, alguém me ajuda:
$(x - 3) \times (x - 2) + x \times \frac{x - 3}{2} = (x - 2) \times (x - 2)$
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Answer 1

$(x - 3) \: . \: (x - 2) + x \: . \: \frac{x - 3}{2} = (x - 2) \: . \: (x - 2)$

$x {}^{2} - 2x - 3x + 6 + \frac{x \: . \: (x - 3)}{2} = (x - 2) {}^{2}$

$x {}^{2} - 2x - 3x + 6 + \frac{x {}^{2} - 3x }{2} = x {}^{2} - 4x + 4$

$- 2x - 3x + 6 + \frac{x {}^{2} - 3x }{2} = - 4x + 4$

$- 5x + 6 + \frac{x {}^{2} - 3x }{2} = - 4x + 4 \: \: \: . \: (2)$

$- 10x + 12 + x {}^{2} - 3x = - 8x + 8$

$-1 3x + 12 + x {}^{2} = - 8x + 8$

$- 13x + 12 + x {}^{2} + 8x - 8 = 0$

$- 5x + 4 + x {}^{2} = 0$

$x {}^{2} - 5x + 4 = 0$

$\boxed{a = 1 \: ,\: b = - 5 \: ,\: c = 4}$

$x = \frac{ - b± \sqrt{b {}^{2} - 4ac } }{2a}$

$x = \frac{ - ( - 5)± \sqrt{( - 5) {}^{2} - 4 \: . \: 1 \: . \: 4 } }{2 \: . \: 1}$

$x = \frac{5± \sqrt{25 - 16} }{2}$

$x = \frac{5± \sqrt{9} }{2}$

$x = \frac{5±3}{2}$

$x = \frac{5 + 3}{2} = \frac{8}{2} = \boxed{4}$

$x = \frac{5 - 3}{2} = \frac{2}{2} = \boxed{1}$

$\boxed{S = \left \{1\: , \:4\right \}}$

Att. NLE Top Shotta