Final answer:
To solve the quadratic equation 4x² - 52x + 169 = 122, it is necessary to use the quadratic formula after rearranging it to the standard form 4x² - 52x + 47 = 0. By substituting the values into the formula, we can find the two solutions.
Step-by-step explanation:
The question involves solving a quadratic equation of the form ax² + bx + c = 0. To solve the equation 4x² - 52x + 169 = 122, we first need to bring the equation to the standard form by subtracting 122 from both sides, resulting in 4x² - 52x + 47 = 0. We then apply the quadratic formula, which for an equation ax² + bx + c = 0 is x = (-b ± √(b² - 4ac)) / (2a). Plugging the coefficients a = 4, b = -52, and c = 47 into the formula, we get two solutions for x which are the solutions to the quadratic equation.