Question

If 2(x-3)^2 = 288, then what will be the value of x?

Answer 1

$\huge \sf \pink{Your \: Question}$

$2(x - 3) {}^{2} = 288$

$\sf \pink{solution = }$

$2(x - 3) {}^{2} = 288 \\ using \: identity \: (a - b) {}^{2} = \\ a {}^{2} + b {}^{2} - 2ab \\ 2(x {}^{2} + (3) {}^{2} - 2 \times x\times 3) = 288 \\ 2(x {}^{2} + 9 - 6x) = 288 \\ 2(x {}^{2} - 6x + 9) = 288 \\ x {}^{2} - 6x + 9 = \frac{288}{2} \\ x {}^{2} - 6x + 9 = 144 \\ x { }^{2} - 6x + 9 - 144 = 0 \\ x {}^{2} - 6x - 135 = 0 \\by \: middle \: term \: splitting \\ \\ x {}^{2} - 15x + 9x - 135 \\ x(x - 15) + 9(x - 15) \\( x + 9)(x - 15) = 0 \\ therefore \\ x = - 9 \: or \: 15 \\ \\ value \: of \: x = - 9 \: and \: 15$