How do you solve #x^2+6x+9=-32#?

Answer 1

#x = -3+-4sqrt(2)i#

The left hand side here is a perfect square trinomial, but the right hand side is negative, so only has an imaginary square root.

We find:

#x^2+6x+9 = (x+3)^2#

Hence:

#(x+3)^2 = -32#

So:

#x+3 = +-sqrt(-32) = +-sqrt(32)i = +-4sqrt(2)i#
Subtract #3# from both sides to get:
#x = -3+-4sqrt(2)i#
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Answer 2

To solve the equation (x^2 + 6x + 9 = -32), follow these steps:

  1. Start by adding 32 to both sides of the equation to move all terms to one side: [x^2 + 6x + 9 + 32 = 0] [x^2 + 6x + 41 = 0]

  2. Now, use the quadratic formula to find the solutions for (x): [x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}]

For the equation (ax^2 + bx + c = 0), in our case, (a = 1), (b = 6), and (c = 41).

  1. Plug in the values into the quadratic formula: [x = \frac{{-6 \pm \sqrt{{6^2 - 4(1)(41)}}}}{{2(1)}}]

  2. Simplify under the square root: [x = \frac{{-6 \pm \sqrt{{36 - 164}}}}{2}] [x = \frac{{-6 \pm \sqrt{{-128}}}}{2}] [x = \frac{{-6 \pm 8i\sqrt{2}}}{2}]

  3. Split into two solutions, one with the plus sign and one with the minus sign: [x = \frac{{-6 + 8i\sqrt{2}}}{2}] [x = \frac{{-6 - 8i\sqrt{2}}}{2}]

So, the solutions for (x) are: [x = -3 + 4i\sqrt{2}] [x = -3 - 4i\sqrt{2}]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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