How do you solve #x(x+2)+3=0# by completing the square?

Answer 1
#0 = x(x+2)+3 = x^2 + 2x + 3 = (x+1)^2+2#. Subtracting 2 from both sides, we get #(x+1)^2 = -2#. If you square any real number you will get a positive value, so there are no real solutions to the problem.
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Answer 2

To solve (x(x+2)+3=0) by completing the square, follow these steps:

  1. Rewrite the equation in the form (ax^2 + bx + c = 0).
  2. Group the terms and rearrange to isolate the squared term and the linear term.
  3. Complete the square by adding and subtracting ((\frac{b}{2})^2) inside the parentheses.
  4. Rewrite the expression as a perfect square trinomial.
  5. Solve for (x) by taking the square root of both sides and isolating (x).
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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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