What is the intermediate step in the form left parenthesis, x, plus, a, right parenthesis, squared, equals, b(x+a)

Question

2
=b as a result of completing the square for the following equation?
x, squared, equals, minus, 2, x, plus, 63
x
2
=
−2x+63

Answer 1

To complete the square for the equation \( x^2 = -2x + 63 \), we first rearrange it into a standard form:

1. Move the \( -2x \) term to the left side: \[ x^2 + 2x = 63 \]

2. Now, to complete the square, we take the coefficient of \( x \) (which is 2), divide it by 2 and square it: \[ \left( \frac{2}{2} \right)^2 = 1 \]

3. Add this squared value to both sides of the equation: \[ x^2 + 2x + 1 = 63 + 1 \]

4. This simplifies to: \[ (x + 1)^2 = 64 \]

Now, the intermediate step after completing the square is: \[ (x + 1)^2 = 64 \]

This is the form you were looking for.