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Rearrange the equation so that the x terms and y terms bracketed together, like so: (x^2 - 4x) + (y^2 + 10y) - 115 = 0. Complete the square on both sets of brackets, giving (x - 2)^2 - 4 + (y + 5)^2 - 25 ...

To integrate (32/ x³ + bx) over x we can integrate each part separately. This is because addition of two integrals is the same as integrating the total of the elements. 

So we integrate ...

The discriminant for a quadratic polynomial of the form f(x) = ax^2 + bx + c is given by b^2 - 4ac. If the discriminant is strictly greater than 2, the quadratic has 2 real distinct roots, i.e 2 unique x-...

Le mie vacanze di Natale non sono state particolarmente emozionanti. Alla mia famiglia piace rispettare le tradizioni, quindi ho passato la vigilia coi miei nonni paterni e il giorno di natale con la nonn...

Step 1: To find the points of intersection, we must find where the y and x values are equal. Therefore 5-x=x²-3x+2 where the y-values are equal.

Step 2: Rearrange the above into the quad...