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.
x2 + 2x - 13 = 2 x2 + 2x - 15 = 0 (x + 5)(x - 3) = 0 x + 5 = 0 and x - 3 = 0 so x = -5 and x = 3
x = 4.74 or -2.74
2x = x2 + 4x - 3 x2 + 2x - 3 = 0 (x - 1)(x - 2) = 0
x2 + 2x -6 = 0 x2 + 2x + 1 = 7 (x + 1)2 = 7 x = -1 ± √7
x2+10x+1 = -12+2x x2+10x-2x+1+12 = 0 x2+8x+13 = 0 Solving by using the quadratic equation formula: x = - 4 - or + the square root of 3
x2 - 2x - 5 = 0 x2 - 2x + 1 = 6 (x - 1)2 = 6 x - 1 = ± √6 x = 1 ± √6
x2-2x-3 = 0 (x+1)(x-3) = 0 x = -1 or x = 3
If: x2+2x-3 = 0 Then: x = 1 or x = -3
Simply by using the formula x= -b +/- Underroot of (b2 - 4.a.c) / 2.a 2+x-6=2x+4
x2+10x+1 = -12+2x x2+8x+13 = 0 The solution: x = -4 + the square root of 3 or x = -4 - the square root of 3
x2-2x-10-5 = 0 x2-2x-15 = 0 (x+3)(x-5) = 0 x = -3 or x = 5
y = x2 + 2x + 1zeros are:0 = x2 + 2x + 10 = (x + 1)(x + 1)0 = (x + 1)2x = -1So that the graph of the function y = x + 2x + 1 touches the x-axis at x = -1.