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Simplifying 25 + x(37 + -1x) = 126 25 + (37 * x + -1x * x) = 126 25 + (37x + -1x2) = 126 Solving 25 + 37x + -1x2 = 126 Solving for variable 'x'. Reorder the terms: 25 + -126 + 37x + -1x2 = 126 + -126 Combine like terms: 25 + -126 = -101 -101 + 37x + -1x2 = 126 + -126 Combine like terms: 126 + -126 = 0 -101 + 37x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 101 + -37x + x2 = 0 Move the constant term to the right: Add '-101' to each side of the equation. 101 + -37x + -101 + x2 = 0 + -101 Reorder the terms: 101 + -101 + -37x + x2 = 0 + -101 Combine like terms: 101 + -101 = 0 0 + -37x + x2 = 0 + -101 -37x + x2 = 0 + -101 Combine like terms: 0 + -101 = -101 -37x + x2 = -101 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 = -101 + 342.25 Reorder the terms: 342.25 + -37x + x2 = -101 + 342.25 Combine like terms: -101 + 342.25 = 241.25 342.25 + -37x + x2 = 241.25 Factor a perfect square on the left side: (x + -18.5)(x + -18.5) = 241.25 Calculate the square root of the right side: 15.532224567 Break this problem into two subproblems by setting (x + -18.5) equal to 15.532224567 and -15.532224567.Subproblem 1
x + -18.5 = 15.532224567 Simplifying x + -18.5 = 15.532224567 Reorder the terms: -18.5 + x = 15.532224567 Solving -18.5 + x = 15.532224567 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 = 15.532224567 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = 15.532224567 + 18.5 x = 15.532224567 + 18.5 Combine like terms: 15.532224567 + 18.5 = 34.032224567 x = 34.032224567 Simplifying x = 34.032224567Subproblem 2
x + -18.5 = -15.532224567 Simplifying x + -18.5 = -15.532224567 Reorder the terms: -18.5 + x = -15.532224567 Solving -18.5 + x = -15.532224567 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 = -15.532224567 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = -15.532224567 + 18.5 x = -15.532224567 + 18.5 Combine like terms: -15.532224567 + 18.5 = 2.967775433 x = 2.967775433 Simplifying x = 2.967775433Solution
The solution to the problem is based on the solutions from the subproblems. x = {34.032224567, 2.967775433}
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