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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.

Use The Expression X2 10x 13 To Answer The Following QuestionsPart A What Numeric Expression Should Be Added In Order To Complete The Square For The Given Expre class=
Use The Expression X2 10x 13 To Answer The Following QuestionsPart A What Numeric Expression Should Be Added In Order To Complete The Square For The Given Expre class=

Sagot :

Given the expression below

[tex]x^2+10x-13=0[/tex]

The general form of a quadratic equation is

[tex]ax^2+bx+c=0[/tex]

Using the completing the square method,

[tex]\begin{gathered} x^2+10x-13=0 \\ x^2+10x=13 \end{gathered}[/tex]

Where b =10 from the given equation

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

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

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

By completing the square

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

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

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