Q. \(x^2 – 6x = 0\)
Answer
We solve \(x^2-6x=0\) by factoring:
\[
x^2-6x=x(x-6)=0
\]
So \(x=0\) or \(x=6\).
Final result: \(x=0, 6\).
Detailed Explanation
We want to solve the equation
\[
x^2 – 6x = 0
\]
Step 1: Factor the left-hand side.
Both terms on the left share a factor of \(x\). Factor out \(x\):
\[
x^2 – 6x = x(x – 6)
\]
Step 2: Use the zero-product rule.
The equation becomes
\[
x(x – 6) = 0
\]
So either \(x = 0\) or \(x – 6 = 0\).
Step 3: Solve each case.
Case 1: If \(x = 0\), then that is a solution.
Case 2: If \(x – 6 = 0\), then add \(6\) to both sides:
\[
x – 6 = 0
\]
\[
x = 6
\]
Final answer:
\[
x = 0 \quad \text{or} \quad x = 6
\]
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Algebra FAQ
How do I factor \(x^2-6x=0\)?
Factor out \(x\): \(x^2-6x=x(x-6)\). Then solve \(x(x-6)=0\).
What are the solutions of \(x^2-6x=0\)?
Set each factor to zero: \(x=0\) or \(x-6=0\Rightarrow x=6\).
Can I solve it using the quadratic formula?
Rewrite as \(x^2-6x+0=0\). Then \(a=1,b=-6,c=0\). Solutions: \(x=\frac{6\pm\sqrt{36}}{2}=0,6\).
What is the greatest common factor (GCF) of the terms?
The GCF of \(x^2\) and \(-6x\) is \(x\). So \(x^2-6x=x(x-6)\).
What does factoring tell me about the roots?
Since \(x(x-6)=0\), the roots correspond to when each factor is zero: \(x=0\) and \(x=6\).
How do I check my answers quickly?
Substitute: If \(x=0\), \(0-0=0\). If \(x=6\), \(36-36=0\). Both satisfy the equation.
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