12x-4y+9z+2y =12x-2y+9z
3x multiplied by (12x plus 9) is:3x(12x + 9)= (3x * 12x) + (3x * 9)= 36x2 + 27x
The equation is equivalent to: -3x2 - 12x - 1 = 0 [you could change signs to get 3x2 + 12x + 1 = 0 but that is not required] The discriminant is (-12)2 - 4*(-3)(-1) = 144 - 12 = 132
x2 + 12x + 27 = (x + 9)(x + 3)
6x2 + 7x = 56x2 + 7x - 5 = 0x =[ -7 ± √[72 - 4(6)(-5)] ]/2(6)x = [-7 ± √(49 + 120)]/12x = (-7 ± √ 169)/12x = (-7 ± 13)/12x = (-7 + 13)/12 or x = (-7 - 13)/12x = 6/12 = 1/2 orx = -20/12 = - 5/3
It is x^2 + 12x or x(x + 12).
-5 + 12x = 18x + 7Subtract 7 from each side:-12 + 12x = 18xSubtract 12x from each side:-12 = 6xDivide each side by 6:-2 = x
9x + 2 = 12x + 14 -3x = 12 x = -4
4x2 is 8+ 12x + 3 collect like terms, 8+3= 11, 12x+11 to solve for x, transpose the 11 to the other side of the = sign, 12x=-11, divide by 12, x=-11/12
2x + 6x + 4x = 12x
x2 + 12x - 11 = x2 + 12x + (12/2)2 - (12/2)2 - 11 = (x + 6)2 - 47
1/2 + 5/6 + 2/3 + 3/12 = x 12(1/2 + 5/6 + 2/3 + 3/12 = x) 6 + 10 + 8 + 3 = 12x 16 + 11 = 12x 25 = 12x 25/12
Factor. X^2 + 12X X(X + 12) = 0 X = 0 ------------- X + 12 = 0 X = - 12 --------------
12x + 17 = 7 Subtract 17 from both sides: 12x = -10 Divide both sides by 12: x = -10/12 = -5/6
12x^3+17x^2+5x=0x(12x^2+17x+5)=0x(x+1)(12x+5)=0x=0x=-1x=-5/12
12x+15p-6p+11x = 12x+11x+15p-6p = (12+11)x+(15-6)p = 23x + 9p
Think of this a 12 x-rays + 5 x-rays Makes 17 x-rays. 12x+5x=17x