How do you solve using the completing the square method #-2x^2 - 7x + 4#?

Answer 1

# -1/2 and 4#

Transform the equation for easier computation --> #2x^2 + 7x - 4 = 0#. Divide both sides by 2. #x^2 + (7x)/2 = 2# #x^2 + (7x)/2 + (7/4)^2 = 2 + 49/16# #(x + 7/4)^2 = 81/16# #(x + 7/4) = +- 9/4# #x = 7/4 +- 9/4 = (7 +- 9)/4# x = 4 and #x = -2/4 = -1/2#
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Answer 2

To solve the quadratic equation -2x^2 - 7x + 4 using the completing the square method, follow these steps:

  1. First, ensure that the coefficient of the x^2 term is 1. Since the coefficient is already -2, divide the entire equation by -2 to get x^2 + (7/2)x - 2.

  2. Rewrite the equation in the form (x + p)^2 + q, where p is half the coefficient of x and q is the constant term.

  3. In this case, p = (7/2) / 2 = 7/4 and q = -2.

  4. Rewrite the equation as (x + 7/4)^2 - 2.

  5. Expand (x + 7/4)^2 to get x^2 + (7/2)x + (49/16).

  6. Rewrite the equation as x^2 + (7/2)x + (49/16) - (32/16).

  7. Combine the terms to get x^2 + (7/2)x + (17/16).

  8. The vertex form of the quadratic equation is (x + 7/4)^2 - 17/16.

Therefore, the solutions for the equation -2x^2 - 7x + 4 using the completing the square method are x = (-7 ± √17)/2.

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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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