How do you solve #x^2-30=0# using the quadratic formula?
We must convert our quadratic into standard form in order to use the quadratic formula:
We already have our quadratic in this format:
Therefore
Next, we apply the formula for quadratics:
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To solve the equation (x^2 - 30 = 0) using the quadratic formula, follow these steps:
- Identify the coefficients (a), (b), and (c) in the equation (ax^2 + bx + c = 0). In this case, (a = 1), (b = 0), and (c = -30).
- Substitute the values of (a), (b), and (c) into the quadratic formula: (x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}).
- Plug in the values: (x = \frac{{-0 \pm \sqrt{{0^2 - 4 \cdot 1 \cdot (-30)}}}}{{2 \cdot 1}}).
- Simplify under the square root: (x = \frac{{\pm \sqrt{{0 + 120}}}}{2}).
- Further simplify: (x = \frac{{\pm \sqrt{{120}}}}{2}).
- Simplify the square root: (x = \frac{{\pm \sqrt{{4 \cdot 30}}}}{2}).
- Extract the perfect square: (x = \frac{{\pm 2\sqrt{{30}}}}{2}).
- Simplify: (x = \pm \sqrt{{30}}).
So, the solutions to the equation (x^2 - 30 = 0) are (x = \sqrt{30}) and (x = -\sqrt{30}).
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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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