Q. \(x^2 = 49\).
Answer
To solve \(x^2=49\), take square roots of both sides.
\[
x=\pm\sqrt{49}=\pm 7
\]
So the solutions are \(x=7\) or \(x=-7\).
Detailed Explanation
We are given the equation
\[ x^{2} = 49. \]
Step 1: Take the square root of both sides.
Because \(x^{2}\) is a square, we use the square root property:
\[ \sqrt{x^{2}} = \sqrt{49}. \]
This gives two possible solutions, since \(x\) could be positive or negative:
\[ x = \pm \sqrt{49}. \]
Step 2: Evaluate the square root.
\[ \sqrt{49} = 7. \]
So the solutions become:
\[ x = 7 \quad \text{or} \quad x = -7. \]
Final Answer:
\[ x = 7 \text{ or } x = -7. \]
See full solution
Algebra FAQ
What are the solutions to \(x^2=49\)?
Solve \(x^2-49=0\) to get \(x=\pm 7\).
Why do both \(x=7\) and \(x=-7\) work?
Because squaring removes sign: \(({-7})^2=(7)^2=49\).
How do I solve \(x^2=49\) using square roots?
Take square roots: \(x=\sqrt{49}=7\) and also the negative root \(x=-7\).
What does \(\sqrt{x^2}\) equal?
\(\sqrt{x^2}=|x|\), so the equation \(x^2=49\) becomes \(|x|=7\).
How do I check my answers?
Substitute: \(7^2=49\) and \(({-7})^2=49\), so both are correct.
What’s the difference between \(x^2=49\) and \(x=\pm 7\)?
\(x^2=49\) implies \(x=\pm 7\). The equation \(x=\pm 7\) is the equivalent solved form.
Solve x²=49 with easy steps now.
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