For this case we have the following expression:
[tex]x ^ 2-4x + 10 = 4x + 10[/tex]
We follow the steps below:
We subtract 4x on both sides of the equation:
[tex]x ^ 2-4x + 10-4x = 4x + 10-4x\\x ^ 2-8x + 10 = 10[/tex]
We subtract 10 from both sides of the equation:
[tex]x ^ 2-8x + 10-10 = 10-10\\x ^ 2-8x = 0[/tex]
Now, we must complete squares.
When we have an equation of the form:
[tex]ax ^ 2 + bx + c = 0[/tex], if we want to complete squares we must subtract c on both sides of the equation obtaining:
[tex]ax ^ 2 + bx + c-c = -c\\ax ^ 2 + bx = -c[/tex]
The square is completed by adding to both sides of the equation: [tex](\frac{b}{2})^{2}[/tex]
So, we have left:
[tex]ax^2+bx + (\frac {b} {2})^{2} = - c + (\frac {b} {2}) ^ {2}[/tex]
In the given expression we have:
[tex]a = 1\\b = -8\\c = 0[/tex]
And to complete the square we have:
[tex](\frac {b} {2}) ^ {2} = (\frac {-8} {2}) ^ {2} = 16[/tex]
Rewriting we have:
[tex]x ^ 2-8x + 16 = 16[/tex]
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:
[tex]-4-4 = -8\\-4 * -4 = 16[/tex]
So, we have:
[tex](x-4) (x-4) = 16\\(x-4) ^ 2 = 16[/tex]
Answer:
The intermediate step is to complete squares
[tex](x-4) ^ 2 = 16[/tex]
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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