Find two number that multiply to 140 and add to 6

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Denote Numbers: Let's denote the two numbers as x and y. We are given two equations based on the problem statement: 1. The product of the two numbers is 140: x * y = 140 2. The sum of the two numbers is 6: x + y = 6 We need to find the values of x and y that satisfy both equations.Express y in terms of x: From the sum equation x + y = 6, we can express y in terms of x: y = 6 - x.Substitute into product equation: Substitute y = 6 - x into the product equation x * y = 140 to get a quadratic equation in terms of x: x * (6 - x) = 140Expand and rewrite quadratic form: Expand the left side of the equation and write it in standard quadratic form: x * 6 - x^2 = 140 -x^2 + 6x = 140Set quadratic equation to zero: Move all terms to one side to set the quadratic equation to zero: -x^2 + 6x - 140 = 0Use quadratic formula: Since the quadratic equation is not easily factorable, we can use the quadratic formula to find the values of x. The quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a), where a = -1, b = 6, and c = -140.Calculate discriminant: Calculate the discriminant Δ = b^2 - 4ac: Δ = 6^2 - 4*(-1)*(-140) Δ = 36 - 560 Δ = -524 Since the discriminant is negative, there are no real solutions to the equation. This means there is a math error in our previous steps or the problem statement might be incorrect as it is not possible for two real numbers to multiply to 140 and add to 6.

Find two number that multiply to $140$ and add to $6$

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Find two number that multiply to $140$ and add to $6$