Question

Let x^2+17x=-5 What values make an equivalent number sentences after completing the square? (Do not simply your answers)

Answer 1

[TeX] (x+\frac{17}{2})^{2}=\frac{269}{4} [/TeX]

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.