Question

solve the equation $x^2 + 4x + 3 = 0$ by completing the square.
drag numbers to the lines to complete the solution to the equation.

step 1: $x^2 + 4x + 3 = 0$

step 2: $(x^2 + 4x + \underline{quad}) + \underline{quad} + 3 = 0$

step 3: $(x + \underline{quad})^2 = \underline{quad}$

step 4: $x + \underline{quad} = \pm \underline{quad}$

solution: $x = \underline{quad}$ and $x = \underline{quad}$

Explanation:

Step1: Complete the square term

To complete the square for $x^2+4x$, take half of 4 (which is 2), square it to get 4. Add and subtract this value:
$(x^2 + 4x + 4) + (-4) + 3 = 0$

Step2: Rewrite as squared binomial

Simplify the constants and rewrite the quadratic as a perfect square:
$(x + 2)^2 = 1$

Step3: Take square root of both sides

Apply the square root property to both sides:
$x + 2 = \pm 1$

Step4: Solve for x

Solve for x by subtracting 2 from both sides for both cases:
For $x + 2 = 1$: $x = 1 - 2 = -1$
For $x + 2 = -1$: $x = -1 - 2 = -3$

Answer:

Step 2 blanks: $4$, $-4$
Step 3 blanks: $2$, $1$
Step 4 blanks: $2$, $1$
Solution blanks: $-1$, $-3$

Final solutions: $x=-1$ and $x=-3$