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Solve the following quadratic equation using the perfect square trinomial pattern: x2+10x+25=0
.(1 point)
x=
Remaining Attempts : 3
.(1 point)
x=
Remaining Attempts : 3
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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 can recognize that the left-hand side can be factored as follows:
The expression \(x^2 + 10x + 25\) can be rewritten as:
\[
(x + 5)^2 = 0
\]
Now, to solve for \(x\), we will take the square root of both sides:
\[
x + 5 = 0
\]
Subtracting 5 from both sides gives:
\[
x = -5
\]
Thus, the solution to the equation \(x^2 + 10x + 25 = 0\) is:
\[
\boxed{-5}
\]
The expression \(x^2 + 10x + 25\) can be rewritten as:
\[
(x + 5)^2 = 0
\]
Now, to solve for \(x\), we will take the square root of both sides:
\[
x + 5 = 0
\]
Subtracting 5 from both sides gives:
\[
x = -5
\]
Thus, the solution to the equation \(x^2 + 10x + 25 = 0\) is:
\[
\boxed{-5}
\]
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