How do you solve the equation 8x^2 – 64x = 0?

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How to Solve the Equation 8x² – 64x = 0

To solve the quadratic equation 8x² – 64x = 0, we can follow these steps:

Step 1: Factor the Equation

First, we can factor out the common term from both parts of the equation:

8x(x - 8) = 0

Step 2: Set Each Factor to Zero

Next, we set each factor equal to zero:

8x = 0
x - 8 = 0

Step 3: Solve for x

From the first factor:

  • 8x = 0: Dividing both sides by 8 gives us x = 0.

From the second factor:

  • x – 8 = 0: Adding 8 to both sides gives us x = 8.

Conclusion

Thus, the solutions for the equation 8x² – 64x = 0 are:

  • x = 0
  • x = 8

So the final answer is: x = 0 and x = 8.

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