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sertanlavr [38]
3 years ago
8

Does the equation x2 - 10x + y2 - 6y = -30 intersect the x-axis?

Mathematics
1 answer:
Dmitriy789 [7]3 years ago
5 0
Intersecting the x axis means y is 0
plug y=0 in the equation and solve for x to see if there are real solutions
x^2-10x+0+0=-30
x^2-10x+30=0
this cannot be factored, so let's see if b^2-4ac is bigger than 0
10^2-4*1*30=-20
so the solutions for this equation are not real numbers, therefore the answer is no.
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Start by subtracting 7 from both sides. Then, divide by -12 to solve for x. Finally, simplify the fraction.

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\large\boxed{x=-\frac{5}{6}}

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