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Simplifying x = -0.125x2 + 5.75x + 71 Reorder the terms: x = 71 + 5.75x + -0.125x2 Solving x = 71 + 5.75x + -0.125x2 Solving for variable 'x'. Reorder the terms: -71 + x + -5.75x + 0.125x2 = 71 + 5.75x + -0.125x2 + -71 + -5.75x + 0.125x2 Combine like terms: x + -5.75x = -4.75x -71 + -4.75x + 0.125x2 = 71 + 5.75x + -0.125x2 + -71 + -5.75x + 0.125x2 Reorder the terms: -71 + -4.75x + 0.125x2 = 71 + -71 + 5.75x + -5.75x + -0.125x2 + 0.125x2 Combine like terms: 71 + -71 = 0 -71 + -4.75x + 0.125x2 = 0 + 5.75x + -5.75x + -0.125x2 + 0.125x2 -71 + -4.75x + 0.125x2 = 5.75x + -5.75x + -0.125x2 + 0.125x2 Combine like terms: 5.75x + -5.75x = 0.00 -71 + -4.75x + 0.125x2 = 0.00 + -0.125x2 + 0.125x2 -71 + -4.75x + 0.125x2 = -0.125x2 + 0.125x2 Combine like terms: -0.125x2 + 0.125x2 = 0.000 -71 + -4.75x + 0.125x2 = 0.000 Begin completing the square. Divide all terms by 0.125 the coefficient of the squared term: Divide each side by '0.125'. -568 + -38x + x2 = 0 Move the constant term to the right: Add '568' to each side of the equation. -568 + -38x + 568 + x2 = 0 + 568 Reorder the terms: -568 + 568 + -38x + x2 = 0 + 568 Combine like terms: -568 + 568 = 0 0 + -38x + x2 = 0 + 568 -38x + x2 = 0 + 568 Combine like terms: 0 + 568 = 568 -38x + x2 = 568 The x term is -38x. Take half its coefficient (-19). Square it (361) and add it to both sides. Add '361' to each side of the equation. -38x + 361 + x2 = 568 + 361 Reorder the terms: 361 + -38x + x2 = 568 + 361 Combine like terms: 568 + 361 = 929 361 + -38x + x2 = 929 Factor a perfect square on the left side: (x + -19)(x + -19) = 929 Calculate the square root of the right side: 30.479501308 Break this problem into two subproblems by setting (x + -19) equal to 30.479501308 and -30.479501308.Subproblem 1
x + -19 = 30.479501308 Simplifying x + -19 = 30.479501308 Reorder the terms: -19 + x = 30.479501308 Solving -19 + x = 30.479501308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = 30.479501308 + 19 Combine like terms: -19 + 19 = 0 0 + x = 30.479501308 + 19 x = 30.479501308 + 19 Combine like terms: 30.479501308 + 19 = 49.479501308 x = 49.479501308 Simplifying x = 49.479501308Subproblem 2
x + -19 = -30.479501308 Simplifying x + -19 = -30.479501308 Reorder the terms: -19 + x = -30.479501308 Solving -19 + x = -30.479501308 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + x = -30.479501308 + 19 Combine like terms: -19 + 19 = 0 0 + x = -30.479501308 + 19 x = -30.479501308 + 19 Combine like terms: -30.479501308 + 19 = -11.479501308 x = -11.479501308 Simplifying x = -11.479501308Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.479501308, -11.479501308}
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