How do you solve #x^2 - x =30# using the quadratic formula?
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To solve the equation (x^2 - x = 30) using the quadratic formula, which is (x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}), where (a), (b), and (c) are the coefficients of the quadratic equation (ax^2 + bx + c = 0), we first rewrite the equation in the standard quadratic form (ax^2 + bx + c = 0). Here, (a = 1), (b = -1), and (c = -30).
Substituting these values into the quadratic formula:
[x = \frac{{-(-1) \pm \sqrt{{(-1)^2 - 4(1)(-30)}}}}{{2(1)}}]
[x = \frac{{1 \pm \sqrt{{1 + 120}}}}{2}]
[x = \frac{{1 \pm \sqrt{121}}}{2}]
[x = \frac{{1 \pm 11}}{2}]
So, the solutions for (x) are (x = \frac{{1 + 11}}{2}) and (x = \frac{{1 - 11}}{2}), which simplify to (x = 6) and (x = -5), respectively.
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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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