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Solve for $x$ . $\newline$ $x^2 = 1$ $\newline$ $\newline$ Write your answer in simplified, rationalized form. $\newline$ $x =$ or $x =$ $\newline$

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Solve a quadratic equation using square roots

Full solution

Q. Solve for

x

.

\newline

x^2 = 1

\newline

\newline

Write your answer in simplified, rationalized form.

\newline

x =

______ or

x =

______

\newline

Finding values of `x:` To solve the equation `x^2 = 1,` we need to find the values of `x` that when squared give us `1`. We can do this by taking the square root of both sides of the equation.
Taking the square root: Taking the square root of both sides of the equation `x^2 = 1` gives us √(x^2) `=` √1.
Considering positive and negative roots: The square root of `x^2` is `x,` and the square root of `1` is `1`. However, we must consider both the positive and negative square roots of `1,` since `(-1)^2` also equals `1`. Therefore, we have `x = 1` and `x =` -1.
Checking the first solution: We now have two possible solutions for `x: x = 1` or `x = -1`. We should check both solutions to ensure they satisfy the original equation.
Checking the second solution: Checking the first solution, `x = 1:` If we substitute `x` with `1` in the original equation, we get `(1)^2 = 1,` which simplifies to `1 = 1`. This is true, so `x = 1` is a valid solution.
Valid solutions: Checking the second solution, `x = -1:` If we substitute `x` with `-1` in the original equation, we get `(-1)^2 = 1,` which simplifies to `1 = 1`. This is true, so `x = -1` is also a valid solution.
Both solutions, `x = 1` and `x = -1,` satisfy the original equation `x^2 = 1`. Therefore, the final answer is `x = 1` or `x =` -1.

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