How do you complete the square to solve #-x^2-2x+3= 0#?
Solutions:
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The left side of the equation now has a perfect square trinomial.
Take each side's square root.
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To solve the quadratic equation (-x^2 - 2x + 3 = 0) by completing the square, follow these steps:
- Move the constant term to the other side of the equation:
(-x^2 - 2x = -3)
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Make sure the coefficient of the (x^2) term is 1. If it's not, divide all terms by the coefficient of (x^2). In this case, the coefficient is already -1, so no change is needed.
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Rewrite the equation with space for adding the square of half the coefficient of (x). The coefficient of (x) is -2, so half of it is -1. Square this value to get 1, and add it to both sides of the equation:
(-x^2 - 2x + 1 = -3 + 1)
- Factor the left side of the equation:
(-(x + 1)^2 = -2)
- Divide both sides of the equation by -1 to isolate the squared term:
((x + 1)^2 = 2)
- Take the square root of both sides:
[x + 1 = \pm \sqrt{2}]
- Solve for (x):
[x = -1 \pm \sqrt{2}]
So, the solutions to the equation (-x^2 - 2x + 3 = 0) are (x = -1 + \sqrt{2}) and (x = -1 - \sqrt{2}).
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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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