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Simplifying 59x + 2596 + 59x = x2 + 44x Reorder the terms: 2596 + 59x + 59x = x2 + 44x Combine like terms: 59x + 59x = 118x 2596 + 118x = x2 + 44x Reorder the terms: 2596 + 118x = 44x + x2 Solving 2596 + 118x = 44x + x2 Solving for variable 'x'. Combine like terms: 118x + -44x = 74x 2596 + 74x + -1x2 = 44x + x2 + -44x + -1x2 Reorder the terms: 2596 + 74x + -1x2 = 44x + -44x + x2 + -1x2 Combine like terms: 44x + -44x = 0 2596 + 74x + -1x2 = 0 + x2 + -1x2 2596 + 74x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 2596 + 74x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2596 + -74x + x2 = 0 Move the constant term to the right: Add '2596' to each side of the equation. -2596 + -74x + 2596 + x2 = 0 + 2596 Reorder the terms: -2596 + 2596 + -74x + x2 = 0 + 2596 Combine like terms: -2596 + 2596 = 0 0 + -74x + x2 = 0 + 2596 -74x + x2 = 0 + 2596 Combine like terms: 0 + 2596 = 2596 -74x + x2 = 2596 The x term is -74x. Take half its coefficient (-37). Square it (1369) and add it to both sides. Add '1369' to each side of the equation. -74x + 1369 + x2 = 2596 + 1369 Reorder the terms: 1369 + -74x + x2 = 2596 + 1369 Combine like terms: 2596 + 1369 = 3965 1369 + -74x + x2 = 3965 Factor a perfect square on the left side: (x + -37)(x + -37) = 3965 Calculate the square root of the right side: 62.968245966 Break this problem into two subproblems by setting (x + -37) equal to 62.968245966 and -62.968245966.Subproblem 1
x + -37 = 62.968245966 Simplifying x + -37 = 62.968245966 Reorder the terms: -37 + x = 62.968245966 Solving -37 + x = 62.968245966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37' to each side of the equation. -37 + 37 + x = 62.968245966 + 37 Combine like terms: -37 + 37 = 0 0 + x = 62.968245966 + 37 x = 62.968245966 + 37 Combine like terms: 62.968245966 + 37 = 99.968245966 x = 99.968245966 Simplifying x = 99.968245966Subproblem 2
x + -37 = -62.968245966 Simplifying x + -37 = -62.968245966 Reorder the terms: -37 + x = -62.968245966 Solving -37 + x = -62.968245966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '37' to each side of the equation. -37 + 37 + x = -62.968245966 + 37 Combine like terms: -37 + 37 = 0 0 + x = -62.968245966 + 37 x = -62.968245966 + 37 Combine like terms: -62.968245966 + 37 = -25.968245966 x = -25.968245966 Simplifying x = -25.968245966Solution
The solution to the problem is based on the solutions from the subproblems. x = {99.968245966, -25.968245966}
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