Question

X square + X - 306 is equal to zero solve by completing square method​

Answer 1

Answer:

${x}^{2} + x - 306 = 0 \\ {x}^{2} + x = 306.....(1) \\ third \: term = ( \frac{1}{2} \times coefficient \: of \: x) ^{2} \\ = ( \frac{1}{2} \times 1) ^{2} \\ = \frac{1}{4} \\ adding \: \frac{1}{4} \: on \: both \: sides \: of \: equation \: \\ (1) \: we \: find: \\ {x}^{2} + x + \frac{1}{4} = 306 + \frac{1}{4} \\ (x + \frac{1}{2} )^{2} = \frac{306 \times 4 + 1}{4} \\ (x + \frac{1}{2} )^{2} = \frac{1224 + 1}{4} \\ (x + \frac{1}{2} )^{2} = \frac{1225}{4} \\ x + \frac{1}{2} = \pm \: \sqrt{ \frac{1225}{4} } \\ x + \frac{1}{2} = \pm \: \frac{35}{2} \\ x = \pm \: \frac{35}{2} - \frac{1}{2} \\ x = \pm \: \frac{35 - 1}{2} \\ x = \pm \frac{34}{2} \\ x = \pm \: 17 \\ hence \: x = - 17 \: or \: x = 17.$