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Find positive roots of x^2+(x+1)^2=313

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The SOLUTION is given below

{x}^{2} + {(x + 1)}^{2} = 313 \\ {x}^{2} + {x}^{2} + 1 + 2x = 313 \\ 2 {x}^{2} + 2x + 1 - 313 = 0 \\ 2 {x}^{2} + 2x - 312 = 0 \\ so \: \: easily \: \: solve \: \: quardritic \: \: equation
x^2 + x - 156=0
x^2 + 13X - 12x - 156
x (x + 13) -12(x + 13)
(x + 13) (x - 12)
so
x= -13 & 12

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