Question

Completing the square method sucks!!

Answer 1

$\huge\underline\purple{Answer ☘}$

$4x {}^{2} + 3x + 5 = 0 \\ \\ dividing \: by \: 4... \\ \frac{4x {}^{2} }{4} + \frac{3x}{4} + \frac{5}{4} = 0 \\ x {}^{2} + \frac{3x}{4} + \frac{5}{4} = 0 \\ \\ we \: know \: that... \\ \: (a + b) {}^{2} = a {}^{2} + b {}^{2} + 2ab \\ \\ here... \\ 2ab = \frac{3x}{4} \\ = > 2xb = \frac{3x}{4} \: \: \: \: \: \: \: \: \: (a = x) \\ 2b = \frac{3}{4} \\ b = \frac{3}{4} \times \frac{1}{2} = \frac{3}{8}$

nσw ín σur єquαtíσn...

$x {}^{2} + \frac{3x}{4} + \frac{5}{4} = 0 \\ \\adding \: and \: subtracting \: (\frac{3}{8}){}^{2} \\ \\ x {}^{2} + \frac{3x}{4} + \frac{5}{4} + ( \frac{3}{8} ) {}^{2} { - ( \frac{3}{8} })^{2} = 0 \\ \\ x {}^{2} + \frac{3x}{4} + (\frac{3}{8} ) {}^{2} + \frac{5}{4} - ( \frac{3}{8} ) {}^{2} = 0 \\ \\ (x + \frac{3}{8} ) {}^{2} + \frac{5}{4 } - ( \frac{3}{8} ) {}^{2} = 0 \\ \\ (x + \frac{3}{8} ) {}^{2} = (\frac{3}{8} ) {}^{2} - \frac{5}{4} \\ \\ (x + \frac{3}{8} ) {}^{2} = \frac{9}{64} - \frac{5}{4} \\ \\ (x + \frac{3}{8} ) {}^{2} = \frac{9 - 5(16)}{64} \\ \\ (x + \frac{3}{8} ) {}^{2} = \frac{9 - 80}{64} \\ \\ (x + \frac{3}{8} ) {}^{2} = \frac{ - 71}{64}$

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