Given that 52 - x2 + x = 10, then -52 + x2 - x + 10 = x2 - x - 42 = (x - 7)(x + 6) = 0. Therefore, x = 7 or -6.
x2 + x - 30 = (x + 6)(x - 5)
x2 + 2y = 52 + 2*2 = 25 + 4 = 29
x = +5 or -5
x2 + 13x = -30 ∴ x2 + 13x + 30 = 0 ∴ (x + 3)(x + 10) = 0 ∴ x ∈ {-3, -10}
x2 + x2 = 2x2
Complete the squares: x2 - 10x + 25 + y2 + 4y + 4 - 52 = 25 + 4 = 29 x2 - 10x + 25 + y2 + 4y + 4 = 52 + 29 = 81 So the radius is sqrt(81) = 9
(2 pi) x sqrt(30)
x2 + 11x + 30 = 0 (x + 5)(x + 6) = 0 so the roots are -5 and -6
5. A circle with centre (0,0) has equation: x2 + y2 = radius2 With: x2 + y2 = 25 = 52 The radius is 5.
x - x2 - 9x + 14 = 0 ; whence, x2 + 8x = 14 , x2 + 8x + 16 = 30 , and x + 4 = ±√30 . Therefore, x = ±√30 - 4 .
6x3 - x2 + 17 = 2x2 + 47 6x3 - x2 - 2x2 = 47 - 17 x2(6x - 1 - 2) = 30 this is the simplest factorisation.