Math, asked by talha382, 9 hours ago

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

Answers

Answered by XxBeingLegendxX
81

 \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

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