2xsquare-6x+3=0 by completing square method

Mathematics

1 answer:

Arturiano [62]3 years ago

5 0

Answer:

x = 2.36603 or 0.633975

Step-by-step explanation:

Here we want to solve the quadratic equation using the completing the square method.

2x^2-6x + 3 = 0

divide through by 2 first;

x^2 -3x + 3/2 = 0

x*2 -3x = -3/2

Half the x term will be -3/2 and squaring it is 9/4

we add this to both sides

x^2-3x/2 + 9/4 = -3/2 + 9/4

(x-3/2)^2 = 3/4

Finding square root of both sides

x-3/2 = √(3/4)

x = 3/2 ± √(3/4)

x = 3/2 + √(3/4) or x = 3/2-√(3/4)

which becomes

x = 2.36603 or 0.633975

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Find the sum of a finite geometric sequence from n=1 to n=8, using the expression -2(3)^n-1

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$\bf \qquad \qquad \textit{sum of a finite geometric sequence}
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S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad 
\begin{cases}
n=n^{th}\ term\\
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\end{cases}
\\\\\\
\sum\limits_{n=1}^{8}~-2(3)^{n-1}~~
\begin{cases}
n=8\\
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