x2 - 2x - 13 = 0
x2 - 2x + 1 = 14
(x - 1)2 = 14
x - 1 = ±√14
x = 1 ±√14
x ≈ {4.742, -2.742}
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x2 + 2x + 2 = 0 Use the quadratic formula: x = (-2 +- sqrt(4 - 8))/2 x = (-2 +- 2i)/2 = -1 +- i
No real roots
2x^2 + 8x + 3 = 0
0
2x + y = 5 . . . thus y = 5 - 2x x2 - y2= 3 . . . . now substitute for y in this equation. x2 - (5 - 2x)2 = 3 . . . and after expansion this becomes, x2 - 25 + 20x - 4x2 = 3 -3x2 + 20x - 28 = 0 . . . and this factors as, (-3x + 14)(x - 2) = 0 Then, x = 2 , x = 14/3 When x = 2, then 2x + y = 5 gives the result y = 1. When x = 14/3 then 2x + y = 5 gives the result y = -13/3.