Answer:
The equation x²+12x+43=0 is a quadratic equation that can be solved by factoring or using the quadratic formula.
Factoring the equation:
x²+12x+43=(x+7)(x+6)=0
x+7=0 or x+6=0
x=-7 and x=-6
Therefore, the solutions for the equation are x=-7 and x=-6.
Alternatively, you can use the quadratic formula:
x = (-b± √(b²-4ac))/2a
Where a=1, b=12, c=43
x = (-12± √(12²-4143))/2*1
x = (-12± √(144-172))/2
x = (-12± √(-28))/2
x = (-12± i*√28)/2
x = (-12+ i2√7)/2 or x = (-12- i2√7)/2
These solutions are complex numbers, x = (-6+2i√7) or x = (-6-2i√7)