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Complete the square for the following equation: 2x^2+6x-3=0

2x 2 +6x-3=0To begin, we need to make sure x 2 is by itself, meaning that we divide the whole equation by 2. So from here we get (2x 2 +6x-3=0) / 2 = x 2 +3x-3/2=0. Now as we have got the x 2 on its own, we ...
Answered by • Maths tutor
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Find the exact solution of the following equation: e^(4x-3) = 11

x= (3 + ln(11))/4
SE
Answered by Sarah E. • Maths tutor
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I am struggling understanding how to differentiate negative indices. I get confused with the power increasing or decreasing.

Hi there, this is a common confusion so don't worry. It is helpful to write out a number line when differentiating and drawing an arrow to show which way the power is moving. <---- differentiate----3 -2 -...
LB
Answered by Lucy B. • Maths tutor
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The first three terms of an arithmetic series are p, 5p – 8, and 3p + 8 respectively. (a) Show that p=4 (b) Find the value of the 50th term in the series.

(a) If the sequence = p , 5p-8 and 3p+8 is an arithmetic sequence then the difference between successive terms must be constant.e.g. (5p-8)-(p) = (3p+8)-(5p-8)=> 4p-8 = -2p+16 => 6p = 24 => p=24/6 =...
DS
Answered by Daniel S. • Maths tutor
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An arithmetic progression has a tenth term (a10) = 11.1 and a fiftieth term (a50) = 7.1 Find the first term (a) and the common difference (d). Also find the sum of the first fifty terms (Sn50) of the progression.

We start off by constructing simultaneous equations as there are two variables - a and d - that we do not know. We use the formula:a n = a + (n-1)di) 11.1 = a + 9dii) 7.1 = a + 49d i) - ii) gives you 4 = - 4...
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