Q. \(x^2 – 8x = 0\)

Q: Solve using the zero product property.

From x(x-8)=0, conclude x=0 or x-8=0\Rightarrow x=8.

Q: Can you solve it with the quadratic formula?

x^2-8x=0. With a=1,b=-8,c=0: x=\frac{8\pm\sqrt{64}}{2}=\frac{8\pm 8}{2}\Rightarrow x=0,8.

Q: What is the discriminant of x^2-8x=0?

\Delta=b^2-4ac=(-8)^2-4(1)(0)=64.

Q: What are the x-intercepts of y=x^2-8x?

Set y=0\Rightarrow x(x-8)=0, so intercepts at (0,0) and (8,0).

Answer

We solve the equation \(x^2-8x=0\) by factoring.

\[
x^2-8x = x(x-8)=0
\]

So \(x=0\) or \(x-8=0\).

\[
x=0 \quad \text{or} \quad x=8
\]

Final result: \(x\in\{0,8\}\)

Detailed Explanation

We want to solve the equation:

\[
x^{2}-8x=0
\]

Step 1: Factor the left-hand side.

The expression \(x^{2}-8x\) has a common factor of \(x\). Factor out \(x\):

\[
x^{2}-8x = x(x-8)
\]

So the equation becomes:

\[
x(x-8)=0
\]

Step 2: Use the zero product property.

If \(x(x-8)=0\), then at least one factor must be zero:

\(x=0\)
\(x-8=0\)

Step 3: Solve the second equation.

\[
x-8=0
\]
Add \(8\) to both sides:

\[
x = 8
\]

Step 4: List all solutions.

The solutions are:

\[
x=0 \quad \text{or} \quad x=8
\]

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Algebra FAQ

Factor \(x^2-8x=0\).

\(x(x-8)=0\).

What are the solutions to \(x^2-8x=0\)?

\(x=0\) or \(x=8\).

Solve using the zero product property.

From \(x(x-8)=0\), conclude \(x=0\) or \(x-8=0\Rightarrow x=8\).

Can you solve it with the quadratic formula?

\(x^2-8x=0\). With \(a=1,b=-8,c=0\): \(x=\frac{8\pm\sqrt{64}}{2}=\frac{8\pm 8}{2}\Rightarrow x=0,8\).

What is the discriminant of \(x^2-8x=0\)?

\(\Delta=b^2-4ac=(-8)^2-4(1)(0)=64\).

What are the x-intercepts of \(y=x^2-8x\)?

Set \(y=0\Rightarrow x(x-8)=0\), so intercepts at \((0,0)\) and \((8,0)\).

Find roots: x^2-8x=0.
Use factoring or set x=0.

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