The equation x² - 9x + 18 = 0 can be solved using the quadratic formula, resulting in two roots: x = 6 and x = 3. Therefore, the solutions to x² + 18 = 9x are x = 6 and x = 3.
Move all terms to one side of the equation to set it to zero:
x² - 9x + 18 = 0
Factor the quadratic expression or use the quadratic formula:
The quadratic formula is x = (-b ± √(b² - 4ac)) / 2a.
For x² - 9x + 18 = 0, a = 1, b = -9, and c = 18.
The quadratic formula becomes x = (9 ± √(81 - 72)) / 2.
Simplifying the expression inside the square root gives x = (9 ± √9) / 2.
Further simplification results in x = (9 ± 3) / 2.
Find the roots:
There are two possible solutions:
x₁ = (9 + 3) / 2 = 6
x₂ = (9 - 3) / 2 = 3
So, the solutions to the equation x² + 18 = 9x are x = 6 and x = 3.