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Simplifying 47x + -2x2 = 4 Solving 47x + -2x2 = 4 Solving for variable 'x'. Reorder the terms: -4 + 47x + -2x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -4 + 47x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2 + -23.5x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -23.5x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -23.5x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -23.5x + x2 = 0 + -2 -23.5x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -23.5x + x2 = -2 The x term is -23.5x. Take half its coefficient (-11.75). Square it (138.0625) and add it to both sides. Add '138.0625' to each side of the equation. -23.5x + 138.0625 + x2 = -2 + 138.0625 Reorder the terms: 138.0625 + -23.5x + x2 = -2 + 138.0625 Combine like terms: -2 + 138.0625 = 136.0625 138.0625 + -23.5x + x2 = 136.0625 Factor a perfect square on the left side: (x + -11.75)(x + -11.75) = 136.0625 Calculate the square root of the right side: 11.664583147 Break this problem into two subproblems by setting (x + -11.75) equal to 11.664583147 and -11.664583147.Subproblem 1
x + -11.75 = 11.664583147 Simplifying x + -11.75 = 11.664583147 Reorder the terms: -11.75 + x = 11.664583147 Solving -11.75 + x = 11.664583147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.75' to each side of the equation. -11.75 + 11.75 + x = 11.664583147 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + x = 11.664583147 + 11.75 x = 11.664583147 + 11.75 Combine like terms: 11.664583147 + 11.75 = 23.414583147 x = 23.414583147 Simplifying x = 23.414583147Subproblem 2
x + -11.75 = -11.664583147 Simplifying x + -11.75 = -11.664583147 Reorder the terms: -11.75 + x = -11.664583147 Solving -11.75 + x = -11.664583147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.75' to each side of the equation. -11.75 + 11.75 + x = -11.664583147 + 11.75 Combine like terms: -11.75 + 11.75 = 0.00 0.00 + x = -11.664583147 + 11.75 x = -11.664583147 + 11.75 Combine like terms: -11.664583147 + 11.75 = 0.085416853 x = 0.085416853 Simplifying x = 0.085416853Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.414583147, 0.085416853}
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