Answer :
Sure, let's solve the given equation step-by-step using the method of completing the square.
The given equation is:
[tex]\[ x^2 + 2x = 19 \][/tex]
### Step 1: Move the constant term to the right side of the equation
[tex]\[ x^2 + 2x + 0 = 19 \][/tex]
### Step 2: Add a number to both sides to complete the square
We need to complete the square on the left-hand side. To do this, take the coefficient of [tex]\( x \)[/tex], which is [tex]\( 2 \)[/tex], divide it by [tex]\( 2 \)[/tex], and then square it:
[tex]\[ \left(\frac{2}{2}\right)^2 = 1 \][/tex]
### Step 3: Add this squared number to both sides of the equation
[tex]\[ x^2 + 2x + 1 = 19 + 1 \][/tex]
### Step 4: The left-hand side now becomes a perfect square trinomial
[tex]\[ (x + 1)^2 = 20 \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{(x+1)^2=20} \][/tex]
So, the answer is:
[tex]\[ \text{B. } (x+1)^2=20 \][/tex]
The given equation is:
[tex]\[ x^2 + 2x = 19 \][/tex]
### Step 1: Move the constant term to the right side of the equation
[tex]\[ x^2 + 2x + 0 = 19 \][/tex]
### Step 2: Add a number to both sides to complete the square
We need to complete the square on the left-hand side. To do this, take the coefficient of [tex]\( x \)[/tex], which is [tex]\( 2 \)[/tex], divide it by [tex]\( 2 \)[/tex], and then square it:
[tex]\[ \left(\frac{2}{2}\right)^2 = 1 \][/tex]
### Step 3: Add this squared number to both sides of the equation
[tex]\[ x^2 + 2x + 1 = 19 + 1 \][/tex]
### Step 4: The left-hand side now becomes a perfect square trinomial
[tex]\[ (x + 1)^2 = 20 \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{(x+1)^2=20} \][/tex]
So, the answer is:
[tex]\[ \text{B. } (x+1)^2=20 \][/tex]
