Question
Solve the following quadratic equation using the perfect square trinomial pattern: x2+10x+25=0
.(1 point)
x=
.(1 point)
x=
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Answered by
GPT-4o mini
To solve the quadratic equation \( x^2 + 10x + 25 = 0 \) using the perfect square trinomial pattern, we first recognize that the left side can be expressed as a square of a binomial.
The equation can be factored as:
\[
(x + 5)^2 = 0
\]
Now, we can set the squared term equal to zero:
\[
(x + 5)^2 = 0
\]
Next, we take the square root of both sides:
\[
x + 5 = 0
\]
Now, solve for \( x \):
\[
x = -5
\]
So the solution to the equation is:
\[
\boxed{-5}
\]
The equation can be factored as:
\[
(x + 5)^2 = 0
\]
Now, we can set the squared term equal to zero:
\[
(x + 5)^2 = 0
\]
Next, we take the square root of both sides:
\[
x + 5 = 0
\]
Now, solve for \( x \):
\[
x = -5
\]
So the solution to the equation is:
\[
\boxed{-5}
\]
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