How do you solve the quadratic equation by completing the square: #2x² - 5x - 12 = 0#?

Answer 1

Solve #y = 2x^2 - 5x - 12 = 0#

x = 5/2 +- 7/2

#2(x^2 - (5x)/2 + 25/4) = 12 + 25/2# #(x^2 - (5x)/2 + 25/4 = 6 + 25/4 = 49/4# #(x - 5/2)^2 = 49/4# --> #(x - 5/2) = +- 7/2#
#x = 5/2 +- 7/2#
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Answer 2

To solve the quadratic equation by completing the square, follow these steps:

  1. Move the constant term to the other side of the equation: 2x² - 5x = 12.
  2. Divide all terms by the coefficient of x² to make the leading coefficient 1: x² - (5/2)x = 6.
  3. Take half of the coefficient of x (in this case, -5/2), square it, and add the result to both sides of the equation: x² - (5/2)x + (-5/4)² = 6 + (-5/4)².
  4. Simplify the left side of the equation: (x - 5/4)² = 6 + 25/16.
  5. Take the square root of both sides to solve for x: x - 5/4 = ±√(6 + 25/16).
  6. Add 5/4 to both sides of the equation: x = 5/4 ± √(6 + 25/16).

The solutions to the quadratic equation 2x² - 5x - 12 = 0 by completing the square are x = 5/4 + √(6 + 25/16) and x = 5/4 - √(6 + 25/16).

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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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