x2 = 8xx2- 8x = 0x(x - 8) = 0x = 0 ;x - 8 = 0x = 8
x2-14x+45=0(x-9)(x-5)=0x-9=0 & x-5=0x=9 & x=5
-18
y = 2x - x2y = 0Since both quantities on the right side are equal to 'y', they're equal to each other.2x - x2 = 0x (2 - x) = 0x = 0and2 - x = 0x = 2The two points of intersection are (0, 0) and (2, 0) .
x2 - 5x + 6 = 0(x - 2) (x - 3) = 0x - 2 = 0 5 × 69 or x - 3 = 0x = 2 or x = 3
x2 - 10x + 25 = 0(x - 5)(x - 5) = 0x - 5 = 0x = 5
x2 - 5x = 0x (x - 5) = 0x = 0andx = 5
x2 = 8xx2- 8x = 0x(x - 8) = 0x = 0 ;x - 8 = 0x = 8
x2-14x+45=0(x-9)(x-5)=0x-9=0 & x-5=0x=9 & x=5
x2-7x+12 = 0 (x-3)(x-4) = 0x=3,4
x2 + 3x + 3 = 7Subtract 7 from each side:x2 + 3x - 4 = 0Factor the left side:(x + 4) (x - 1) = 0x = - 4x = +1
x2 - x + 3 = 0x = [1 +/- sqrt(1-12)]/2 = [1 +/- i*sqrt(11)]/2 where i is the imaginary square root of -1.
x2 + 2x - 15 = 0(x + 5) (x - 3) = 0x = -5x = +3
x2 - 5x = 0Factor the left side:x (x - 5) = 0x = 0x = 5
Factorise: (x - 8)( x + 15) = 0x - 8 = 0 or x + 15 = 0, so x = 8 or -15Check: 64 + 56 = 120 OK; 225 - 105 = 120 OKJob done.
x2 - 7x + 6 = 0(x - 6)(x - 1) = 0x = 6, x = 1
Rearrange: x2 - 4x + 4 = 0Factorise: (x - 2)(x - 2) = 0x = 2Check: 4 + 4 = 4 x 2? Sure does, job done.