Question

Find the roots by completing the square 1 )root2x^2+7x+5root2

Answer 1

$\sqrt{2} {x}^{2} + 7x + 5 \sqrt{2} = 0 \\ {x}^{2} + \frac{7x}{ \sqrt{2} } + \frac{5 \sqrt{2} }{ \sqrt{2} } = 0 \\ {x}^{2} + \frac{7x}{ \sqrt{2} } = - 5 \\ {x}^{2} + \frac{7x}{ \sqrt{2} } + { (\frac{7}{2 \sqrt{2} } })^{2} = 5 + ({ \frac{7}{2 \sqrt{2} } })^{2} \\( {x + \frac{7}{2 \sqrt{2} } })^{2} = 5 + \frac{49}{8} \\( {x + \frac{7}{2 \sqrt{2} } })^{2} = \frac{40 + 49}{8} \\ x + \frac{7}{2 \sqrt{2} } = \sqrt{ \frac{89}{8} } \\ x = \frac{ \sqrt{89} }{2 \sqrt{2} } - \frac{7}{2 \sqrt{2} } \\ x = \frac{ \sqrt{89 } - 7 }{2 \sqrt{2} }$
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