x^(2)-10 x+41=0

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x^(2)-10 x+41=0

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Identify Coefficients: Step Title: Identify the Coefficients Concise Step Description: Identify the coefficients of the quadratic equation, which are the numbers in front of the variables. In this case, the coefficients are 1, -10, and 41. Step Calculation: Coefficients are 1, -10, 41 Step Output: Coefficients: 1, -10, 41Find Factors: Step Title: Find the Factors Concise Step Description: Find two numbers that multiply to 41 (the last term) and add to -10 (the coefficient of the middle term). Step Calculation: Factors of 41 that add up to -10 do not exist since 41 is a prime number and the only factors are 1 and 41, which do not add up to -10. Step Output: No factors foundUse Quadratic Formula: Step Title: Use the Quadratic Formula Concise Step Description: Since the quadratic does not factor neatly, use the quadratic formula to find the roots of the equation. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a). Step Calculation: For the equation x^2 - 10x + 41 = 0, a = 1, b = -10, and c = 41. Plugging these into the quadratic formula gives x = (10 ± √((-10)^2 - 4(1)(41))) / (2(1)) = (10 ± √(100 - 164)) / 2 = (10 ± √(-64)) / 2. Since the discriminant (under the square root) is negative, there are no real solutions. Step Output: No real solutions

$x^{2}-10 x+41=0$

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x2−10x+41=0 x^{2}-10 x+41=0 x2−10x+41=0

$x^{2}-10 x+41=0$