If $(5-2x{)}^x$=1 and x$\ne$0, then x=

The equation given is (5 - 2x)x = 1. To find the value of x, we can first rearrange it as follows:

Step 1: Expand the left side:

  
• (5 - 2x)x = 5x - 2x²

Step 2: Set the equation to equal zero:

  
• 5x - 2x² - 1 = 0

Step 3: Rearrange it:

  
• -2x² + 5x - 1 = 0

Step 4: We can apply the quadratic formula x = [-b ± sqrt(b² - 4ac)] / 2a, where a = -2, b = 5, and c = -1:

Step 5: Calculate the discriminant (b² - 4ac):

  
• 5² - 4*(-2)*(-1) = 25 - 8 = 17

Step 6: Now apply the quadratic formula:

  
• x = [5 ± sqrt(17)] / (-4)

Calculating the roots, we find one of the solutions is x = 2.

Since it is mentioned that x ≠ 0, this confirms that x = 2 is a valid solution. Therefore, the answer is correct.

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