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Simplifying 1792x2 + -99.2x + -2862.48 = 0 Reorder the terms: -2862.48 + -99.2x + 1792x2 = 0 Solving -2862.48 + -99.2x + 1792x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1792 the coefficient of the squared term: Divide each side by '1792'. -1.597366071 + -0.05535714286x + x2 = 0 Move the constant term to the right: Add '1.597366071' to each side of the equation. -1.597366071 + -0.05535714286x + 1.597366071 + x2 = 0 + 1.597366071 Reorder the terms: -1.597366071 + 1.597366071 + -0.05535714286x + x2 = 0 + 1.597366071 Combine like terms: -1.597366071 + 1.597366071 = 0.000000000 0.000000000 + -0.05535714286x + x2 = 0 + 1.597366071 -0.05535714286x + x2 = 0 + 1.597366071 Combine like terms: 0 + 1.597366071 = 1.597366071 -0.05535714286x + x2 = 1.597366071 The x term is -0.05535714286x. Take half its coefficient (-0.02767857143). Square it (0.0007661033164) and add it to both sides. Add '0.0007661033164' to each side of the equation. -0.05535714286x + 0.0007661033164 + x2 = 1.597366071 + 0.0007661033164 Reorder the terms: 0.0007661033164 + -0.05535714286x + x2 = 1.597366071 + 0.0007661033164 Combine like terms: 1.597366071 + 0.0007661033164 = 1.5981321743164 0.0007661033164 + -0.05535714286x + x2 = 1.5981321743164 Factor a perfect square on the left side: (x + -0.02767857143)(x + -0.02767857143) = 1.5981321743164 Calculate the square root of the right side: 1.264172526 Break this problem into two subproblems by setting (x + -0.02767857143) equal to 1.264172526 and -1.264172526.Subproblem 1
x + -0.02767857143 = 1.264172526 Simplifying x + -0.02767857143 = 1.264172526 Reorder the terms: -0.02767857143 + x = 1.264172526 Solving -0.02767857143 + x = 1.264172526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02767857143' to each side of the equation. -0.02767857143 + 0.02767857143 + x = 1.264172526 + 0.02767857143 Combine like terms: -0.02767857143 + 0.02767857143 = 0.00000000000 0.00000000000 + x = 1.264172526 + 0.02767857143 x = 1.264172526 + 0.02767857143 Combine like terms: 1.264172526 + 0.02767857143 = 1.29185109743 x = 1.29185109743 Simplifying x = 1.29185109743Subproblem 2
x + -0.02767857143 = -1.264172526 Simplifying x + -0.02767857143 = -1.264172526 Reorder the terms: -0.02767857143 + x = -1.264172526 Solving -0.02767857143 + x = -1.264172526 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.02767857143' to each side of the equation. -0.02767857143 + 0.02767857143 + x = -1.264172526 + 0.02767857143 Combine like terms: -0.02767857143 + 0.02767857143 = 0.00000000000 0.00000000000 + x = -1.264172526 + 0.02767857143 x = -1.264172526 + 0.02767857143 Combine like terms: -1.264172526 + 0.02767857143 = -1.23649395457 x = -1.23649395457 Simplifying x = -1.23649395457Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.29185109743, -1.23649395457}
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