Question

X^2+3x+1=0 square method solution quadratic equation ​

Answer 1

Step-by-step explanation:

${x}^{2} + 3x + 1 = 0 \\ {x}^{2} + 3x = - 1 \\ add \: {( \frac{3}{2}) }^{2} \: on \: both \: side \\ {x}^{2} + 3x + { (\frac{3}{2}) }^{2} = - 1 + {( \frac{3}{2} )}^{2} \\ {(x + \frac{3}{2}) }^{2} = - 1 + \frac{9}{4} \\ {(x + \frac{3}{2}) }^{2} = \frac{ - 4 + 9}{4} \\ {(x + \frac{3}{2}) }^{2} = \frac{5}{4} \\ x + \frac{3}{2} = \sqrt{ \frac{5}{4} } \\ x + \frac{3}{2} = \frac{ \sqrt{5} }{2} \\ x = \frac{ \sqrt{5} }{2} - \frac{3}{2} \\ x = \frac{ \sqrt{5} - 3 }{2}$

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