Q. \(x^2 – 100 = 0\)

Q: How do you solve x^2-100=0?

Add 100: x^2=100. Then take square roots: x=\pm 10.

Q: What factoring method works for x^2-100?

Use difference of squares: x^2-100=(x-10)(x+10)=0. So x=10 or x=-10.

Q: Why do we get two solutions when taking square roots?

Because x^2=100 implies x=\sqrt{100} or x=-\sqrt{100}. Square roots have plus/minus: x=\pm 10.

Q: How can completing the square be applied here?

It’s already in near-completed form: x^2-100=0\Rightarrow x^2=100. Completing the square adds no extra steps.

Q: What is the general solution pattern for x^2=a?

If x^2=a, then x=\pm\sqrt{a} for a\ge 0. If a<0, solutions are complex.

Q: How do you verify the solutions x=10 and x=-10 quickly?

Substitute: 10^2-100=100-100=0. Also (-10)^2-100=100-100=0.

Answer

We solve the equation \(x^2-100=0\) by adding \(100\) to both sides:

\[
x^2=100
\]

Taking square roots gives two solutions:

\[
x=\pm 10
\]

Final result: \(x=-10\) or \(x=10\).

Detailed Explanation

We want to solve the equation

\[
x^2 – 100 = 0
\]

Step 1: Add 100 to both sides.

This isolates the \(x^2\) term.

\[
x^2 – 100 + 100 = 0 + 100
\]

\[
x^2 = 100
\]

Step 2: Take the square root of both sides.

Because \(x^2 = 100\), \(x\) can be either the positive or negative square root.

\[
x = \sqrt{100} \quad \text{or} \quad x = -\sqrt{100}
\]

Step 3: Evaluate the square root.

\[
\sqrt{100} = 10
\]

So the two solutions are:

\[
x = 10 \quad \text{or} \quad x = -10
\]

Final Answer:

\[
\boxed{x = 10 \text{ or } x = -10}
\]

See full solution

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Algebra FAQ

How do you solve \(x^2-100=0\)?

Add \(100\): \(x^2=100\). Then take square roots: \(x=\pm 10\).

What factoring method works for \(x^2-100\)?

Use difference of squares: \(x^2-100=(x-10)(x+10)=0\). So \(x=10\) or \(x=-10\).

Why do we get two solutions when taking square roots?

Because \(x^2=100\) implies \(x=\sqrt{100}\) or \(x=-\sqrt{100}\). Square roots have plus/minus: \(x=\pm 10\).

How can completing the square be applied here?

It’s already in near-completed form: \(x^2-100=0\Rightarrow x^2=100\). Completing the square adds no extra steps.

What is the general solution pattern for \(x^2=a\)?

If \(x^2=a\), then \(x=\pm\sqrt{a}\) for \(a\ge 0\). If \(a<0\), solutions are complex.

How do you verify the solutions \(x=10\) and \(x=-10\) quickly?

Substitute: \(10^2-100=100-100=0\). Also \((-10)^2-100=100-100=0\).

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