Final answer:
The intermediate step after completing the square for the equation x²-4x+10=4x+10 is (x - 2)² = 4. By taking the square root of both sides and solving for x, we get two solutions: x = 4 and x = 0.
Step-by-step explanation:
The intermediate step in the form (x+a)² = b as a result of completing the square for the equation x²-4x+10=4x+10 is to rearrange the equation to isolate the x-terms on one side. To do this, first, we cancel out the '4x+10' on both sides, since they are identical and therefore simplify to 0. This leaves us with the simplified equation x² - 4x = 0.
To complete the square, we take the coefficient of x, which is -4, divide it by 2, and square it to find the number that needs to be added to both sides of the equation. In this case, (-4/2)² = 4. We then add 4 to both sides to get x² - 4x + 4 = 4. This simplifies to (x - 2)² = 4, which is the intermediate step in the completing the square process.
To find the value of x, we take the square root of both sides, yielding x - 2 = ± 2. Adding 2 to both terms gives us the two possible solutions: x = 2 ± 2, which are x = 4 and x = 0.