The idea is to solve the equation -3x2 + 24x - 19 = 0. You can use the quadratic formula for this, using a = -3, b = 24, c = 19. Or complete the square since dividing by -3 will give us 8x, an even coefficient. -3x2 + 24x - 19 = 0 (add and subtract 48 to the left side) -3x2 + 24x -48 + 29 = 0 (subtract 29 to both sides, and factor out -3) -3(x2 - 8x + 16) = -29 (divide by -3 to both sides) (x - 4)2 = 29/3 x - 4 = ± √(29/3) (add 4 to both sides) x = 4 ± √(29/3) (multiply by 3/3 inside the radical, if you want to rationalize the denominator) x = 4 ± (√87)/3
29 x 19 = 551 I hope this helps you! : )
3 x 29 = 87
19
3 x 3 x 3 x 19 or 3^3 x 19^1
14, 19, 29, 44, 64, etc. 14 + (5 x 1) = 19 19 + (5 x 2) = 29 29 + (5 x 3) = 44 44 + (5 x 4) = 64
1131 = 3 x 13 x 29, 1767 = 3 x 19 x 31. GCF is only 3.
The idea is to solve the equation -3x2 + 24x - 19 = 0. You can use the quadratic formula for this, using a = -3, b = 24, c = 19. Or complete the square since dividing by -3 will give us 8x, an even coefficient. -3x2 + 24x - 19 = 0 (add and subtract 48 to the left side) -3x2 + 24x -48 + 29 = 0 (subtract 29 to both sides, and factor out -3) -3(x2 - 8x + 16) = -29 (divide by -3 to both sides) (x - 4)2 = 29/3 x - 4 = ± √(29/3) (add 4 to both sides) x = 4 ± √(29/3) (multiply by 3/3 inside the radical, if you want to rationalize the denominator) x = 4 ± (√87)/3
29 x 19 = 551 I hope this helps you! : )
2 x 7 x 19 x 29
3 x 29 = 87
19
171 = 3 x 3 x 19.3 x 3 x 19 = 171
3 x 3 x 3 x 19 or 3^3 x 19^1
219
19
The prime factors are: 3 x 3 x 3 x 29