Final answer:
To solve the quadratic equation x² - 24x + 62 = -9x + 6, rearrange the equation, factor the quadratic equation, and solve for x.
Step-by-step explanation:
To solve the quadratic equation x² - 24x + 62 = -9x + 6, we can start by rearranging the equation to bring all terms to one side:
x² - 15x + 56 = 0
Next, we factor the quadratic equation:
(x - 7)(x - 8) = 0
Setting each factor equal to zero, we find the solutions:
x - 7 = 0 ⟼ x = 7
x - 8 = 0 ⟼ x = 8
Therefore, the solutions to the quadratic equation are x = 7 and x = 8.