How do you complete the square to solve #x^2  2x = 15#?
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To complete the square to solve the equation (x^2  2x = 15), follow these steps:
 Move the constant term to the other side of the equation: (x^2  2x  15 = 0).
 Take half of the coefficient of the (x) term, square it, and add it to both sides of the equation: [x^2  2x + (2/2)^2 = 15 + (2/2)^2].
 Simplify both sides: [x^2  2x + 1 = 15 + 1].
 Factor the left side and simplify the right side: [(x  1)^2 = 16].
 Take the square root of both sides: [x  1 = \pm \sqrt{16}].
 Solve for (x): [x = 1 \pm 4].
 Thus, the solutions are (x = 5) and (x = 3).
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To solve the equation x^2  2x = 15 by completing the square, follow these steps:

Move the constant term to the other side of the equation: x^2  2x  15 = 0.

To complete the square, take half of the coefficient of x, square it, and add it to both sides of the equation: x^2  2x + (2/2)^2 = 15 + (2/2)^2.

Simplify both sides of the equation: x^2  2x + 1 = 15 + 1.

Simplify further: (x  1)^2 = 16.

Take the square root of both sides of the equation: √((x  1)^2) = ±√16.

Solve for x: x  1 = ±4.

Add 1 to both sides: x = 1 ± 4.

The solutions are: x = 1 + 4 = 5, x = 1  4 = 3.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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