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Simplifying -1x2 + 37x + -10 = 40 Reorder the terms: -10 + 37x + -1x2 = 40 Solving -10 + 37x + -1x2 = 40 Solving for variable 'x'. Reorder the terms: -10 + -40 + 37x + -1x2 = 40 + -40 Combine like terms: -10 + -40 = -50 -50 + 37x + -1x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -50 + 37x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 50 + -37x + x2 = 0 Move the constant term to the right: Add '-50' to each side of the equation. 50 + -37x + -50 + x2 = 0 + -50 Reorder the terms: 50 + -50 + -37x + x2 = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -37x + x2 = 0 + -50 -37x + x2 = 0 + -50 Combine like terms: 0 + -50 = -50 -37x + x2 = -50 The x term is -37x. Take half its coefficient (-18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. -37x + 342.25 + x2 = -50 + 342.25 Reorder the terms: 342.25 + -37x + x2 = -50 + 342.25 Combine like terms: -50 + 342.25 = 292.25 342.25 + -37x + x2 = 292.25 Factor a perfect square on the left side: (x + -18.5)(x + -18.5) = 292.25 Calculate the square root of the right side: 17.095320997 Break this problem into two subproblems by setting (x + -18.5) equal to 17.095320997 and -17.095320997.Subproblem 1
x + -18.5 = 17.095320997 Simplifying x + -18.5 = 17.095320997 Reorder the terms: -18.5 + x = 17.095320997 Solving -18.5 + x = 17.095320997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = 17.095320997 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = 17.095320997 + 18.5 x = 17.095320997 + 18.5 Combine like terms: 17.095320997 + 18.5 = 35.595320997 x = 35.595320997 Simplifying x = 35.595320997Subproblem 2
x + -18.5 = -17.095320997 Simplifying x + -18.5 = -17.095320997 Reorder the terms: -18.5 + x = -17.095320997 Solving -18.5 + x = -17.095320997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = -17.095320997 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = -17.095320997 + 18.5 x = -17.095320997 + 18.5 Combine like terms: -17.095320997 + 18.5 = 1.404679003 x = 1.404679003 Simplifying x = 1.404679003Solution
The solution to the problem is based on the solutions from the subproblems. x = {35.595320997, 1.404679003}
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