x2 + 49
= x2 - (-49)
= x2 - (-1)(49)
= x2 - (i2)(72)
= x2 - (7i)2
= (x - 7i)(x + 7i)
where i is the imaginary square root of -1.
x2 + 49 = 0 ∴ x2 = -49 ∴ x = 7i
x2+14x+49 = (x+7)(x+7) when factored
51.07142857142857
7
Yes
(x2 + 14x + 49) = (x + 7)2
x2 + 49 = 0 ∴ x2 = -49 ∴ x = 7i
-x2+14x=49
x2 - 14x + 49(x - 7) (x - 7)
x2+14x+49 = (x+7)(x+7) when factored
51.07142857142857
x2 - 14x + 49 = (x - 7)2
7
Yes
49 x2 + 14x = -7 x2 + 14x + 49 = 42 (x + 7)2 = 42 x = -7 ± √42
7
x2 + y - 49 = 0At the x-intercepts, y=0:x2 - 49 = 0(x+7)(x-7) = 0x = -7 and x = +7At the y-intercept, x=0:y - 49 = 0y = 49