Question

Determine the zeroes of 10x2−5=35

Answer 1

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:

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