Question

1.5 assess your understanding
are you prepared? answers are given at the end of these exercises. if you get a wrong answer, read the pages listed in red.

1. to complete the square of $x^{2}+10x$, you would __ (add/subtract) the number __. (pp. a28 - a29)
2. use the square root method to solve the equation $(x - 2)^{2}=9$. (p. a48)

Explanation:

1.

Step1: Recall the formula for completing the square

For a quadratic expression of the form $x^{2}+bx$, to complete the square, we add $(\frac{b}{2})^{2}$. Here $b = 10$, so $(\frac{10}{2})^{2}=25$ and we add the number.

Step2: Determine the operation

We add the number 25 to complete the square of $x^{2}+10x$.

Step1: Apply the square - root property

If $(x - 2)^{2}=9$, then $x-2=\pm\sqrt{9}$.

Step2: Simplify the square - root

Since $\sqrt{9} = 3$, we have $x - 2=\pm3$.

Step3: Solve for x

When $x - 2=3$, then $x=3 + 2=5$. When $x - 2=-3$, then $x=-3 + 2=-1$.

Answer:

add; 25

2.