Question
Find the solutions to x^2 - 14x + 49 = 0
Answers
Answered by
GPT-4o mini
To solve the quadratic equation \( x^2 - 14x + 49 = 0 \), we can start by recognizing that this quadratic can be factored.
We can observe that:
\[
x^2 - 14x + 49 = (x - 7)^2
\]
This is because:
\[
(x - 7)(x - 7) = x^2 - 7x - 7x + 49 = x^2 - 14x + 49
\]
Setting this equal to zero gives us:
\[
(x - 7)^2 = 0
\]
Taking the square root of both sides yields:
\[
x - 7 = 0
\]
Solving for \( x \) gives:
\[
x = 7
\]
Since this is a perfect square, there is one unique solution:
\[
\boxed{7}
\]
We can observe that:
\[
x^2 - 14x + 49 = (x - 7)^2
\]
This is because:
\[
(x - 7)(x - 7) = x^2 - 7x - 7x + 49 = x^2 - 14x + 49
\]
Setting this equal to zero gives us:
\[
(x - 7)^2 = 0
\]
Taking the square root of both sides yields:
\[
x - 7 = 0
\]
Solving for \( x \) gives:
\[
x = 7
\]
Since this is a perfect square, there is one unique solution:
\[
\boxed{7}
\]