Question

$(x - 3)(2x + 1) = (x - 2) {}^{2}$
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Answer 1

$\huge\mathfrak\red{Answer}$

$(x - 3)(2x + 1) = ( {x - 2)}^{2} \\ x(2x + 1) - 3(2x + 1) = {(x - 2)}^{2} \\ 2 {x}^{2} + x - 6x - 3 = {(x - 2)}^{2} \\ 2 {x}^{2} - 5x - 3 = {x}^{2} + 4 - 4x \\ 2 {x}^{2} - {x}^{2} - 5x + 4x - 3 - 4 = 0 \\ {x}^{2} - x - 7 = 0 \\ \\ now \: solve \: this \: quadratic \: eq \: for \: x \\ \\ a = 1 \\ b = - 1 \\ c = - 1 \\ \\ x = \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a} or \frac{ - b - \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ x = \frac{ - ( - 1) + \sqrt{ {( - 1)}^{2} -4 (1) ( - 1)} }{2(1)} \\ \\ x = \frac{1 - \sqrt{1 + 4} }{2} \: or \: \frac{1 + \sqrt{1 + 4} }{2} \\ \\ x = \frac{1 - \sqrt{5} }{2} \: or \: \frac{1 + \sqrt{5} }{2}$