How do you solve the quadratic equation by completing the square: #2x² - 5x - 12 = 0#?
Solve x = 5/2 +- 7/2
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To solve the quadratic equation by completing the square, follow these steps:
- Move the constant term to the other side of the equation: 2x² - 5x = 12.
- Divide all terms by the coefficient of x² to make the leading coefficient 1: x² - (5/2)x = 6.
- 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.
- Simplify the left side of the equation: (x - 5/4)² = 6 + 25/16.
- Take the square root of both sides to solve for x: x - 5/4 = ±√(6 + 25/16).
- 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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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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