Final answer:
To solve the equation 3(m+2)²+10(m+2)+3=0, we can use the quadratic formula to find the value of m. The solutions to this equation are approximately -3.333 and -2.333.
Step-by-step explanation:
To solve the equation 3(m+2)²+10(m+2)+3=0, we can use the quadratic formula. First, set the equation equal to 0:
3(m+2)²+10(m+2)+3=0.
Expand and simplify the equation:
3(m²+4m+4)+10m+20+3=0.
Combine like terms:
3m²+22m+23=0.
Now, we can use the quadratic formula:
m = (-b ± √(b²-4ac))/(2a).
Plugging in the values a=3, b=22, and c=23 into the formula, we can calculate the solutions:
m = (-22 ± √(22²-4(3)(23)))/(2(3)).
Simplifying this expression gives us two solutions: m ≈ -3.333 and m ≈ -2.333.