(x-11)^2=(x-7)(x-9)

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x-11)^2 = (x-7)(x-9)

This equation presents a quadratic equation in a slightly disguised form. Here's how to solve it:

1. Expand both sides of the equation:

• Left side: (x-11)^2 = (x-11)(x-11) = x^2 - 22x + 121
• Right side: (x-7)(x-9) = x^2 - 16x + 63

Now the equation becomes: x^2 - 22x + 121 = x^2 - 16x + 63

2. Simplify the equation:

Subtract x^2 from both sides: -22x + 121 = -16x + 63

3. Isolate the x term:

Add 22x to both sides: 121 = 6x + 63

Subtract 63 from both sides: 58 = 6x

4. Solve for x:

Divide both sides by 6: x = 58/6 = 29/3

Therefore, the solution to the equation (x-11)^2 = (x-7)(x-9) is x = 29/3.