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How do I solve quadratic equation by completing the square : X^2 - 4X = 5

We have X 2 - 4X = 5, write the expression on the left side as X 2 - 2•2X = 5. Then we would need extra term 4 to complete the square, so adding 4 on the both sides gives us, X 2 - 2•2X + 4 = 5 +4. Simplify ...
RK
Answered by Rabin K. • Maths tutor
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Integrate cos(4x)+16x^3 with respect to x

This is a simple integration, integrating each individual term with respect to x.For the cos(4x), you should use 'integration by substitution' as it is a function of a function.cos(4x) = cos(u) and u = 4x wh...
AC
Answered by Aadil C. • Maths tutor
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When calculating a question with a double integral question between two different ranges which range relates to which integration variable.

When doing double integration with two arbitrary variables, for example 'x' and 'y' look at the Integration on the inside and integrate the function between the given range. For example if the integrand is t...
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Answered by Piranavan V. • Maths tutor
3544 Views

How do I differentiate (e^(2x)+1)^3?

You might be tempted to start by expanding the brackets, but in this case it's much easier to use the chain rule. This is the rule that, to differentiate f(g(x)), we find f'(g(x))*g'(x). In other words, to d...
AH
Answered by Alfie H. • Maths tutor
4480 Views

It is given that n satisfies the equation 2*log(n) - log(5*n - 24) = log(4). Show that n^2 - 20*n + 96 = 0.

Given 2log a n - log a (5 n -24) = log a (4) , we can rearrange to have all the "2logs" on one side and the "logs" on the other.So, 2log a n = log a (4) + log a (5 n -24) . Using the laws...
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Answered by Cara S. • Maths tutor
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