Question

solve by factoring.
(x + 2)(x + 2)=1

Explanation:

Step1: Expand the left - hand side

$(x + 2)(x + 2)=x^{2}+4x + 4$. So the equation becomes $x^{2}+4x + 4=1$.

Step2: Rearrange to standard quadratic form

Subtract 1 from both sides: $x^{2}+4x+4 - 1=0$, which simplifies to $x^{2}+4x + 3=0$.

Step3: Factor the quadratic equation

We need two numbers that multiply to 3 and add up to 4. The numbers are 1 and 3. So $x^{2}+4x + 3=(x + 1)(x+3)=0$.

Step4: Solve for x

Set each factor equal to zero:
If $x + 1=0$, then $x=-1$.
If $x + 3=0$, then $x=-3$.

Answer:

$x=-1$ or $x=-3$