How do you complete the square to solve #x^2 - 2x - 35 = 0#?
Along the way, I applied the inequality of difference of squares:
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To complete the square to solve (x^2 - 2x - 35 = 0), follow these steps:
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Move the constant term to the other side of the equation: [x^2 - 2x = 35]
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Take half of the coefficient of (x) (-2), square it, and add it to both sides of the equation: [x^2 - 2x + (-2/2)^2 = 35 + (-2/2)^2] [x^2 - 2x + 1 = 35 + 1]
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Simplify both sides: [x^2 - 2x + 1 = 36]
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Rewrite the left side as a squared binomial: [(x - 1)^2 = 36]
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Take the square root of both sides: [x - 1 = \pm \sqrt{36}]
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Solve for (x): [x - 1 = \pm 6] [x = 1 \pm 6]
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Simplify: [x = 1 + 6 = 7] or [x = 1 - 6 = -5]
Therefore, the solutions to the equation (x^2 - 2x - 35 = 0) are (x = 7) and (x = -5).
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To complete the square to solve the quadratic equation x^2 - 2x - 35 = 0:
-
Move the constant term to the other side of the equation: x^2 - 2x = 35
-
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 = 35 + (-2/2)^2 x^2 - 2x + 1 = 35 + 1
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Simplify both sides of the equation: x^2 - 2x + 1 = 36
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Rewrite the left side of the equation as a perfect square trinomial: (x - 1)^2 = 36
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Take the square root of both sides of the equation: x - 1 = ±√36
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Solve for x: x - 1 = ±6 x = 1 ± 6
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The solutions are: x = 1 + 6 = 7 x = 1 - 6 = -5
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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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