Question

X square minus root 2 + 1 X + root 2 = 0 find to find the zeros in completing square method​

Answer 1

Answer:

$\huge{\boxed{\boxed{\underline{\sf{x=0\:and\:-1}}}}}$

Step-by-step explanation:

$\huge{\boxed{\underline{\mathfrak{SOLUTION-}}}}$

$\huge{\boxed{\boxed{\underline{\sf{COMPLETING\:SQUARE\:METHOD-}}}}}$

${x}^{2} - \sqrt{2} + x + \sqrt{2} = 0 \\ {x}^{2} + x = 0 \\ dividing \: both \: side \: coeficient \: of \: x \\ {x}^{2} + x = 0 \\ both \: side \: adding \: ({ \frac{b}{2a} })^{2} = ( { \frac{1}{2 \times 1} })^{2} = \frac{1}{4} \\ {x}^{2} + \frac{1}{4} + x = \frac{1}{4} \\( x + \frac{1}{2})^{2} = \frac{1}{4} \\ x + \frac{1}{2} = + - \sqrt{ \frac{1}{4} } \\ x + \frac{1}{2} = + - \frac{1}{2} \\ first \: we \: take \: + \frac{1}{4} \\ = ) x + \frac{1}{2} = \frac{1}{2} \\ = ) x = 0 - - - - - 1st \: zeroes \\ we \: take \frac{ - 1}{2} \\ = )x + \frac{1}{2} = \frac{ - 1}{2} \\ = )x = \frac{ - 1}{2} - \frac{1}{2} \\ = ) x = \frac{ - 1 - 1}{2} \\ = )x = \frac{ - 2}{2} \\ = )x = - 1 - - - - - 2nd \: zeroes$

☆Another short method to solve:

$\huge{\boxed{\boxed{\underline{\sf{MIDDLE\:TERM\:SPLITING-}}}}}$

$x^{2}+x=0\\take\:common\:from \:them\\x(x+1)=0\\x=0-----1st\:zeroes\\x+1=0\\x=-1-----2nd\:zeroes$

$\huge{\boxed{\boxed{\underline{\sf{x=0\:and\:-1}}}}}$