Answer:
[TeX] (x+\frac{17}{2})^{2}=\frac{269}{4} [/TeX]
Step-by-step explanation:
Given the expression:
[TeX] x^2+17x=-5 [/TeX]
To complete the square,
First Step: Identify the Coefficient of x.
Coefficient of x=17
Second Step: Divide the coefficient of x by 2.
Third Step: Square your result from the second step.
This gives:
[TeX] (\frac{17}{2})^{2}[/TeX]
Fourth Step: Add your result to both sides if the equation.
[TeX] x^2+17x+(\frac{17}{2})^{2}=-5+(\frac{17}{2})^{2} [/TeX]
Fifth Step:Express the left hand side as a square
[TeX] (x+\frac{17}{2})^{2}=-5+(\frac{17}{2})^{2} [/TeX]
Sixth Step:Simplify the Right Hand Side
[TeX] (x+\frac{17}{2})^{2}=\frac{269}{4} [/TeX]
These are the values that make an equivalent number sentence.
