How do you complete the square to solve #x^2 - 2x - 35 = 0#?

Answer 1
#0 = x^2-2x-35#
#= x^2-2x+1-1-35#
#=(x-1)^2-36#
#= (x-1)^2-6^2#
#= ((x-1)-6)((x-1)+6)#
#= (x-7)(x+5)#
So #x=7# or #x=-5#

Along the way, I applied the inequality of difference of squares:

#(a^2-b^2) = (a-b)(a+b)#
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Answer 2

To complete the square to solve (x^2 - 2x - 35 = 0), follow these steps:

  1. Move the constant term to the other side of the equation: [x^2 - 2x = 35]

  2. 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]

  3. Simplify both sides: [x^2 - 2x + 1 = 36]

  4. Rewrite the left side as a squared binomial: [(x - 1)^2 = 36]

  5. Take the square root of both sides: [x - 1 = \pm \sqrt{36}]

  6. Solve for (x): [x - 1 = \pm 6] [x = 1 \pm 6]

  7. 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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Answer 3

To complete the square to solve the quadratic equation x^2 - 2x - 35 = 0:

  1. Move the constant term to the other side of the equation: x^2 - 2x = 35

  2. 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

  3. Simplify both sides of the equation: x^2 - 2x + 1 = 36

  4. Rewrite the left side of the equation as a perfect square trinomial: (x - 1)^2 = 36

  5. Take the square root of both sides of the equation: x - 1 = ±√36

  6. Solve for x: x - 1 = ±6 x = 1 ± 6

  7. The solutions are: x = 1 + 6 = 7 x = 1 - 6 = -5

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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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