Answer :
To determine which of the given values of [tex]\( x \)[/tex] satisfy the equation [tex]\((x-3)(x+9) = -27\)[/tex], we substitute each value into the equation and check:
1. Substitute [tex]\( x = -9 \)[/tex]:
[tex]\[ (x-3)(x+9) = (-9-3)(-9+9) = (-12)(0) = 0 \][/tex]
This does not satisfy the equation [tex]\((x-3)(x+9) = -27\)[/tex].
2. Substitute [tex]\( x = -3 \)[/tex]:
[tex]\[ (x-3)(x+9) = (-3-3)(-3+9) = (-6)(6) = -36 \][/tex]
This does not satisfy the equation [tex]\((x-3)(x+9) = -27\)[/tex].
3. Substitute [tex]\( x = 0 \)[/tex]:
[tex]\[ (x-3)(x+9) = (0-3)(0+9) = (-3)(9) = -27 \][/tex]
This satisfies the equation [tex]\((x-3)(x+9) = -27\)[/tex].
4. Substitute [tex]\( x = 6 \)[/tex]:
[tex]\[ (x-3)(x+9) = (6-3)(6+9) = (3)(15) = 45 \][/tex]
This does not satisfy the equation [tex]\((x-3)(x+9) = -27\)[/tex].
Hence, the solution to the equation [tex]\((x-3)(x+9) = -27\)[/tex] among the given options is:
- [tex]\( x = 0 \)[/tex]
1. Substitute [tex]\( x = -9 \)[/tex]:
[tex]\[ (x-3)(x+9) = (-9-3)(-9+9) = (-12)(0) = 0 \][/tex]
This does not satisfy the equation [tex]\((x-3)(x+9) = -27\)[/tex].
2. Substitute [tex]\( x = -3 \)[/tex]:
[tex]\[ (x-3)(x+9) = (-3-3)(-3+9) = (-6)(6) = -36 \][/tex]
This does not satisfy the equation [tex]\((x-3)(x+9) = -27\)[/tex].
3. Substitute [tex]\( x = 0 \)[/tex]:
[tex]\[ (x-3)(x+9) = (0-3)(0+9) = (-3)(9) = -27 \][/tex]
This satisfies the equation [tex]\((x-3)(x+9) = -27\)[/tex].
4. Substitute [tex]\( x = 6 \)[/tex]:
[tex]\[ (x-3)(x+9) = (6-3)(6+9) = (3)(15) = 45 \][/tex]
This does not satisfy the equation [tex]\((x-3)(x+9) = -27\)[/tex].
Hence, the solution to the equation [tex]\((x-3)(x+9) = -27\)[/tex] among the given options is:
- [tex]\( x = 0 \)[/tex]
