But it has two perfectly good solutions!
They happen to be complex numbers ... with real and imaginary parts ...
but that shouldn't be a show stopper.
x = 3 + i sqrt(15)
x = 3 - i sqrt(15)
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(x - 7) is.
x2 - 14x = 7 add (14/2)2 to both sidesx2 - 14x 72 = 7 + 72(x - 7)2 = 56 take the square root to both sidesx - 7 = +&- sq. root of 56x = - 7 +&- 2(sq. root of 14)
Notice that the left side of the equation is a perfect square (x - 7)2 = x2 -14x + 49. so (x - 7)2 = 4. Take square root of both sides: x - 7 = ± 2, x = 9, or x = 5.
7x3 + 2x = 607x3 + 2x - 60 = 07x3 - 28 x + 30x - 60 = 07x(x2 - 4) + 30(x - 2) = 07x(x + 2)(x - 2) + 30(x - 2) = 0(x - 2)[7x(x + 2) + 30] = 0(x - 2)(7x2 + 14x + 30) = 0x - 2 = 0 or 7x2 + 14x + 30 = 0x = 2 orx = {-14 +&- square root of [142 - 4(7)(30)]}/(2)(7)x = -14/14 +&- (square root of -644)]/14x = -1 +&- 2i(square root of 161)/14x = -1 +&- (square root of 161)i/7
x2+14x+49 = (x+7)(x+7) when factored