Question

Use the expression x^2 + 10x − 13 to answer the following questions.Part A: What numeric expression should be added in order to complete the square for the given expression?Part B: What expression is equivalent to the given expression after completing the square?Select two answers: one for Part A and one for Part B.

Answer 1

Given the expression below

`x^2+10x-13=0`

The general form of a quadratic equation is

`ax^2+bx+c=0`

Using the completing the square method,

`\begin{gathered} x^2+10x-13=0 \\ x^2+10x=13 \end{gathered}`

Where b =10 from the given equation

`\begin{gathered} \text{Addding (}(b)/(2))^2\text{ to both sides} \\ ie\text{ (}(10)/(2))^2=5^2=25 \\ \text{Add 25 to both sides} \end{gathered}`
`x^2+10x+25=13+25`

For part A, the numerical value to be added is 25

Hence, for part A, the answer is 25-25

By completing the square

`\begin{gathered} x^2+10x+25=13+25 \\ (x+5)^2=38 \\ (x+5)^2-38=0 \end{gathered}`

Hence, for part B, the answer is (x+5)²-38