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4 years ago

2 - 7 ( 4x + 5 ) = -33 + 5x

Mathematics

1 answer:

Olegator [25]4 years ago

4 0

2 - 28x - 35 = -33 + 5x
-33 - 28x = -33 + 5x
-33+33 = 5x+28x
0=33x
x=0

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

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For this case we have the following expression:

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We follow the steps below:

We subtract 4x on both sides of the equation:

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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:

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

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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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