Q. \(x^2=121\)

Q: Why are there two solutions for x^2=121?

Because squaring removes sign. Both 11^2 and (-11)^2 equal 121, so x=\pm 11.

Q: How do you solve x^2=a in general?

If a\ge 0, then \[x^2=a \Rightarrow x=\pm\sqrt{a}\]

Answer

We solve \(x^2=121\) by taking square roots of both sides:

\[
x=\pm \sqrt{121}=\pm 11
\]

Final result: \(x=11\) or \(x=-11\).

Detailed Explanation

We are asked to solve the equation

\[
x^2 = 121
\]

Step 1: Take the square root of both sides.

To undo the squaring, we take square roots of the left and right sides:

\[
\sqrt{x^2} = \sqrt{121}
\]

Step 2: Use the square root rule.

For real numbers, square rooting a square gives the absolute value:

\[
\sqrt{x^2} = \lvert x \rvert
\]

Also, since \(121 = 11^2\), we have \( \sqrt{121} = 11 \). So the equation becomes:

\[
\lvert x \rvert = 11
\]

Step 3: Convert the absolute value equation to two equations.

The equation \( \lvert x \rvert = 11 \) means \(x\) can be \(11\) or \(-11\):

\[
x = 11 \quad \text{or} \quad x = -11
\]

Answer:

The solutions to \(x^2 = 121\) are

\[
x = 11 \text{ and } x = -11
\]

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Algebra FAQ

Solve \(x^2=121\).

\[x=\pm\sqrt{121}=\pm 11\]

What is \( \sqrt{121} \)?

\[\sqrt{121}=11\]

Why are there two solutions for \(x^2=121\)?

Because squaring removes sign. Both \(11^2\) and \((-11)^2\) equal \(121\), so \(x=\pm 11\).

Check solutions: does \(x=11\) satisfy \(x^2=121\)?

\[11^2=121\]

Check solutions: does \(x=-11\) satisfy \(x^2=121\)?

\[(-11)^2=121\]

How do you solve \(x^2=a\) in general?

If \(a\ge 0\), then \[x^2=a \Rightarrow x=\pm\sqrt{a}\]

Solve x²=121 step by step.
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