Solve the equation for all real solutions in simplest form.d, squared, plus, 9, d, plus, 12, equals, minus, 4d 2 +9d+12=−4
Question
Solve the equation for all real solutions in simplest form.
Solution
To solve the equation, we need to simplify it and find the values of d that satisfy the equation.
First, let's rearrange the equation to bring all the terms to one side:
d^2 + 9d + 12 = -4d
Next, let's combine like terms:
d^2 + 9d + 4d + 12 = 0
Simplifying further:
d^2 + 13d + 12 = 0
Now, we can factor the quadratic equation:
(d + 1)(d + 12) = 0
Setting each factor equal to zero:
d + 1 = 0 or d + 12 = 0
Solving for d:
d = -1 or d = -12
Therefore, the real solutions to the equation are d = -1 and d = -12.
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