Solve the following quadratic equation using the perfect square trinomial pattern: x^2+10x+25=0

Question

.(1 point)
x=___

Answer 1

To solve the quadratic equation $x^2+10x+25=0$ using the perfect square trinomial pattern, we can recognize that the left-hand side can be factored.

The expression $x^2+10x+25$ can be rewritten as:

$$(x+5{)}^2$$

This is because:

$$(x+5)(x+5)=x^2+5x+5x+25=x^2+10x+25$$

So, we can rewrite the equation as:

$$(x+5{)}^2=0$$

Next, we take the square root of both sides:

$$x+5=0$$

Now, we solve for $x$:

$$x=-5$$

Thus, the solution is:

$$x=-5$$