How do you solve the equation by factoring and the zero-product rule: #4x^2-25#?
Method 1
factorise by difference of squares
solving for each bracket
Method 2
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To solve the equation 4x^2 - 25 = 0 by factoring and the zero-product rule, you first factor the quadratic expression as a difference of squares: (2x)^2 - 5^2. Then, you can apply the zero-product rule, setting each factor equal to zero:
- (2x + 5) = 0
- (2x - 5) = 0
Solve each equation for x:
-
For (2x + 5) = 0: 2x + 5 = 0 2x = -5 x = -5/2
-
For (2x - 5) = 0: 2x - 5 = 0 2x = 5 x = 5/2
So, the solutions to the equation 4x^2 - 25 = 0 are x = -5/2 and x = 5/2.
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The equation provided, (4x^2 - 25 = 0), can be solved using factoring and the zero-product rule.
First, recognize that (4x^2 - 25) is a difference of squares, which can be factored into ((2x)^2 - 5^2). This factors into ((2x + 5)(2x - 5)).
Now, according to the zero-product rule, if the product of two factors equals zero, then at least one of the factors must equal zero. Therefore, set each factor equal to zero and solve for (x):
-
(2x + 5 = 0): Subtract 5 from both sides: (2x = -5). Divide both sides by 2: (x = -\frac{5}{2}).
-
(2x - 5 = 0): Add 5 to both sides: (2x = 5). Divide both sides by 2: (x = \frac{5}{2}).
Thus, the solutions to the equation (4x^2 - 25 = 0) are (x = -\frac{5}{2}) and (x = \frac{5}{2}).
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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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