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belka [17]
3 years ago
7

Determine the zeroes of 10x2−5=35

Mathematics
1 answer:
OLEGan [10]3 years ago
5 0

Answer:

x = +2, x = -2

Step-by-step explanation:

The equation to solve in this problem is

10x^2-5=35

The first step we do is to subtract 35 on both sides of the equation, so we get:

10x^2-5-35=0\\10x^2-40=0

Now we simplify the equation by dividing both terms by 10:

\frac{10x^2-40}{10}=0\\x^2-4=0

Now we observe that the term on the left is the difference between two squares, so it can be rewritten using the property:

a^2-b^2=(a+b)(a-b)

Where here,

a = x

b = 2

So we can rewrite the equation as:

x^2-4=0\\(x+2)(x-2)=0

And this equation is zero when either one of the two factors is zero, so the two solutions are:

x+2=0\rightarrow x=-2\\x-2=0 \rightarrow x=+2

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