To factor out the greatest common factor (GCF) and solve the quadratic equation \(7x^2 = 56x\), we start by rearranging the equation into standard form. This means we want to set the equation to zero:
-
Rearrange the equation: \[ 7x^2 - 56x = 0 \]
-
Identify the GCF of the terms on the left side. The GCF of \(7x^2\) and \(-56x\) is \(7x\).
-
Factor out the GCF: \[ 7x(x - 8) = 0 \]
-
Set each factor equal to zero: \[ 7x = 0 \quad \text{or} \quad x - 8 = 0 \]
-
Solve for \(x\):
- From \(7x = 0\), we get \(x = 0\).
- From \(x - 8 = 0\), we get \(x = 8\).
So, the solutions to the equation \(7x^2 = 56x\) are: \[ x = 0 \quad \text{and} \quad x = 8. \]
If you have multiple choice options or tables to choose from, look for a table that matches these steps: rearranging the equation, finding the GCF, factoring, and solving for \(x\).
1 answer