Question

Complete the square for the quadratic equation x² +10x+21=0.

A) (x+5)² = =4
B) (x+5)² = =16
C) (x+5)² = =25
D) (x+5)² = 36

Answer 1

To complete the square, the quadratic equation x² + 10x + 21 becomes (x + 5)² = 4. This is achieved by moving the constant term to the right side, halving the linear term's coefficient, squaring it, adding and subtracting it on the left side, and simplifying.

Step-by-step explanation:

To complete the square for the quadratic equation x² + 10x + 21 = 0, we need to follow these steps:

1. Start with the original equation x² + 10x + 21 = 0.
2. Move the constant term to the right side of the equation, getting x² + 10x = -21.
3. Divide the coefficient of the x term by 2 and square it, which is (10/2)² = 25.
4. Add and subtract this number inside the left side of the equation to maintain balance: x² + 10x + 25 - 25 = -21.
5. Recognize the left side as a perfect square trinomial, (x + 5)² - 25 = -21.
6. Add 25 to both sides to isolate the perfect square: (x + 5)² = 4.

The completed square form is option A: (x + 5)² = 4.