%5E2%3D(x-7)(x-9).jpeg "(x-11)^2=(x-7)(x-9)")
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.