Answer:
c. \((x+1)^2=20\)
Step-by-step explanation:
Since, for getting a perfect square on the left side of a quadratic equation we follow the following steps,
Step 1 : Make 1 as the coefficient of \(x^2\).
Step 2 : Add both side the square of a number which is half of the x's coefficient.
Given equation,
\(x^2+2x=19\) -----(1)
Here, the coefficient of \(x^2\) is already one.
And, the middle term is 2,
Half of 2 is 1
Also, 1² = 1
Thus, add 1 on both sides of equation (1),
\(x^2+2x+1 = 19 + 1\)
\((x+1)^2 = 20\) ( Because (a+b)² = a² + 2ab + b² )
⇒ Option C is correct.
