Question

Use complete the square method to rewrite x2 - 6x + 9 = 25 as an

equation with a squared binomial.

Answer 1

To rewrite x² - 6x + 9 = 25 as an equation with a squared binomial, you move the constant to the right side, complete the square by adding (b/2)² to both sides, resulting in the squared binomial equation (x - 3)² = 25.

Step-by-step explanation:

To rewrite the equation x² - 6x + 9 = 25 as an equation with a squared binomial using the complete the square method, follow these steps:

1. Begin with the original equation: x² - 6x + 9 = 25.
2. Move the constant term to the right side of the equation: x² - 6x = 25 - 9.
3. Simplify the equation: x² - 6x = 16.
4. Divide the coefficient of x by 2, and square the result to find the value to complete the square: (-6 / 2)² = (-3)² = 9.
5. Add this value to both sides of the equation to maintain the balance: x² - 6x + 9 = 16 + 9.
6. This gives us a perfect square on the left side of the equation: (x - 3)² = 25.
7. Therefore, the original equation can be rewritten as a squared binomial equation: (x - 3)² = 25.