Let's first simplify both sides of the equation:
2(x+4) - x(x-5) = 7(x-8)
Expanding the left side2x + 8 - x^2 + 5x = 7x - 56
Combine like terms2x + 8 - x^2 + 5x = 7x - 57x + 8 - x^2 = 7x - 56
Now, move all terms to one side of the equation7x + 8 - x^2 - 7x + 56 = -x^2 + 64 = 0
Now, we need to solve for x-x^2 + 64 = -x^2 = -6x^2 = 6x = ± 8
Therefore, the solution to the equation is x = 8 or x = -8.
Let's first simplify both sides of the equation:
2(x+4) - x(x-5) = 7(x-8)
Expanding the left side
2x + 8 - x^2 + 5x = 7x - 56
Combine like terms
2x + 8 - x^2 + 5x = 7x - 5
7x + 8 - x^2 = 7x - 56
Now, move all terms to one side of the equation
7x + 8 - x^2 - 7x + 56 =
-x^2 + 64 = 0
Now, we need to solve for x
-x^2 + 64 =
-x^2 = -6
x^2 = 6
x = ± 8
Therefore, the solution to the equation is x = 8 or x = -8.