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2 years ago

Please answer asap!!

Mathematics

1 answer:

Roman55 [17]2 years ago

3 0

He found 2x.

When you subtract the outer length of the frame from the outer length of the picture you get the length of the actual exposed frame. To find the length on either side if the picture you would divide by 2 because there are 2 X's. Therefore he found 2x

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2 years ago

What is the intermediate step in the form (x+a)2 = b as a result of completing the square for the following

skelet666 [1.2K]

For this case we have the following expression:

$x ^ 2-4x + 10 = 4x + 10$

We follow the steps below:

We subtract 4x on both sides of the equation:

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We subtract 10 from both sides of the equation:

$x ^ 2-8x + 10-10 = 10-10\\x ^ 2-8x = 0$

Now, we must complete squares.

When we have an equation of the form:

$ax ^ 2 + bx + c = 0$ , if we want to complete squares we must subtract c on both sides of the equation obtaining:

$ax ^ 2 + bx + c-c = -c\\ax ^ 2 + bx = -c$

The square is completed by adding to both sides of the equation: $(\frac{b}{2})^{2}$

So, we have left:

$ax^2+bx + (\frac {b} {2})^{2} = - c + (\frac {b} {2}) ^ {2}$

In the given expression we have:

$a = 1\\b = -8\\c = 0$

And to complete the square we have:

$(\frac {b} {2}) ^ {2} = (\frac {-8} {2}) ^ {2} = 16$

Rewriting we have:

$x ^ 2-8x + 16 = 16$

We factor the left side of the equation, that is, we look for two numbers that when added together result in -8 and when multiplied as a result 16. We have:

$-4-4 = -8\\-4 * -4 = 16$

So, we have:

$(x-4) (x-4) = 16\\(x-4) ^ 2 = 16$

Answer:

The intermediate step is to complete squares

$(x-4) ^ 2 = 16$

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