Question

Find the roots (if they exist) of the following
quadratic equations by the method of
completing the square : 4x^2 + x + 15

Answer 1

$4 {x}^{2} + x + 15 = 0 \\ \\ divide \: by \: 4 \\ \\ {x}^{2} + \frac{x}{4} = \frac{ - 15}{4} \\ \\ add \: ( \frac{1}{8})^{2} \: on \: both \: sides \\ \\ {x}^{2} + \frac{x}{4} + ( \frac{1}{8} )^{2} = \frac{ - 15}{4} + ( \frac{1}{8} ) ^{2} \\ \\ (x + \frac{1}{8} ) ^{2} = \frac{ - 15}{4} + \frac{1}{64} \\ \\ (x + \frac{1}{8} ) ^{2} = \frac{ - 240 + 1}{64} \\ \\ x + \frac{1}{8} = \sqrt{ \frac{ - 239}{64} } \\ \\ x = \sqrt{ - 239} \div 8 - \frac{1}{8} \\ \\ x = \frac{ - \sqrt{239 - 1} }{8} \\ \\ or \\ \\ x = \frac{ \sqrt{239} }{8}$