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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.d, squared, plus, 9, d, plus, 12, equals, minus, 4d 2 +9d+12=−4

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Solution 1

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.

This problem has been solved

Solution 2

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.

This problem has been solved

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