Final answer:
To solve the equation, begin by isolating the square root term and eliminating the square root by squaring both sides. This forms a quadratic equation which can be solved by factoring or using the quadratic formula. The solutions to the equation are x = 8 and x = 9.
Step-by-step explanation:
To solve the equation √x - 8 + 8 = x, we can begin by isolating the square root term on one side of the equation. Adding 8 to both sides, we get √x = x - 8. Next, we square both sides of the equation to eliminate the square root. This gives us x = (x - 8)^2. Expanding the squared term, we have x = x^2 - 16x + 64. Rearranging the equation to form a quadratic, we have x^2 - 17x + 64 = 0.
To solve this quadratic equation, we can factor it or use the quadratic formula. Factoring the quadratic gives us (x - 8)(x - 9) = 0. Setting each factor equal to zero, we have x - 8 = 0 and x - 9 = 0. Solving these equations, we find x = 8 and x = 9 as the solutions to the original equation.
Therefore, the correct answer is C. x = 8 and x = 9.