What is the intermediate step in the form (x+a)2 = b as a result of completing the square for the following x2-4x+10=4x+10

For this case we have the following expression:

We follow the steps below:

We subtract 4x on both sides of the equation:

We subtract 10 from both sides of the equation:

Now, we must complete squares.

When we have an equation of the form:

, if we want to complete squares we must subtract c on both sides of the equation obtaining:

The square is completed by adding to both sides of the equation:

So, we have left:

In the given expression we have:

And to complete the square we have:

Rewriting we have:

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:

So, we have:

The intermediate step is to complete squares

The intermediate step in the form (x+a)2 = b as a result of completing the square for the following is (x-4)^2 = 16

Given the equation x^2-4x+10=4x+10

This can also be written as:

x^2-4x+10 - 4x - 10 = 0

x^2 - 8x = 0

To complete the square of the expression, we will add the square of the half of coefficient of x in the equation to both sides

Coefficent of x = -8

Half of the coefficient = -4

Square of the result = (-4)^2 = 16

Add 16 to both sides to have:

x^2 - 8x + 16 = 0+ 16

x^2 - 8x + 16 = 16

(x-4)^2 = 16

Hence the intermediate step in the form (x+a)2 = b as a result of completing the square for the following is (x-4)^2 = 16

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step-by-step explanation: