Question

What is the intermediate step in the form left bracket, x, plus, a, right bracket, squared, equals, b for the equation (x + a)² = b as a result of completing the square?

a) x² + 2ax + a² = b
b) x² + 2ax + a² = b - a²
c) (x + a)² - a² = b
d) (x + a)² = b + a²

Answer 1

The intermediate step in completing the square for the equation (x + a)² = b is x² + 2ax + a² = b.

Step-by-step explanation:

The intermediate step in completing the square for the equation (x + a)² = b involves expanding the squared term and then solving for x. This step is reflected in option a) which is x² + 2ax + a² = b. The process of completing the square makes use of the expanded form of the squared binomial, which allows for easier manipulation and solving of the quadratic equation.

Another method to solve for x would require using the quadratic formula, which is applicable when the equation is in the standard form ax² + bx + c = 0. In completing the square for the equation (x + a)² = b, the intermediate step is to subtract a² from both sides of the equation. This is done to isolate the squared term on one side of the equation.