Question

factorise: (x - 1/2)² = 4

*The answer is -3/2,5/2 ​

Answer 1

Answer:

$({x - \frac{1}{2} })^{2} = 4$

${(x)}^{2} + ( { \frac{1}{2} })^{2} - 2(x)( \frac{1}{2} ) = 4$

${x}^{2} + \frac{1}{4} - x = 4$

${x}^{2} - x = 4 - \frac{1}{4}$

${x}^{2} - x = \frac{16 - 1}{4}$

${x}^{2} - x = \frac{15}{4}$

$4( {x}^{2} - x) = 15$

${4x}^{2} - 4x = 15$

${4x}^{2} - 4x - 15 = 0$

On splitting the middle term

${4x}^{2} + 6x - 10x - 15 = 0$

$2x(2x + 3) - 5(2x + 3)$

$(2x + 3)(2x - 5) = 0$

$2x + 3 = 0$

$2x = - 3$

$x = \frac{ - 3}{2}$

$2x - 5 = 0$

$2x = 5$

$x = \frac{5}{2}$