The equation after completing the square is [tex]x^2 + 13x + \frac{169}4= -3 + \frac{169}4[/tex]
The expression is given as:
[tex]x^2 + 13x = -3[/tex]
Represent the coefficient of x with k.
So, we have:
[tex]k = 13[/tex]
Divide by both sides by 2
[tex]\frac k2 = \frac{13}2[/tex]
Take the square of both sides
[tex](\frac k2)^2 = (\frac{13}2)^2[/tex]
Add the above expression to both sides of the equation [tex]x^2 + 13x = -3[/tex]
So, we have:
[tex]x^2 + 13x + (\frac{13}2)^2= -3 + (\frac{13}2)^2[/tex]
Evaluate the exponents
[tex]x^2 + 13x + \frac{169}4= -3 + \frac{169}4[/tex]
Hence, the equation after completing the square is [tex]x^2 + 13x + \frac{169}4= -3 + \frac{169}4[/tex]
Read more about completing the squares at:
https://brainly.com/question/10449635
