x=-1
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x2+8x+9 = -7 x2+8x+9+7 = 0 x2+8x+16 = 0 (x+4)(x+4) = 0 Therefore: x = -4 and also x = -4 (they both have equal roots)
The possible values for k are -2 and -14 because in order for the line to be tangent to the curve the discriminant must be equal to 0 as follows:- -2x-2 = x2-8x+7 => 6-x2-9 = 0 -14x-2 = x2-8x+7 => -6-x2-9 = 0 Discriminant: 62-4*-1*-9 = 0
x2 + 8x - 9 = 0(x + 9) (x - 1) = 0(x + 9) = 0 . . . . . x = -9(x - 1) = 0 . . . . . x = 1
2x+6x=-9 => 8x=-9=> x=-8/9
8x-2 = -9+7x8x-7x = -9+2x=-7