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Simplifying 0.484x2 + -1.07928x + -0.0036 = 0 Reorder the terms: -0.0036 + -1.07928x + 0.484x2 = 0 Solving -0.0036 + -1.07928x + 0.484x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.484 the coefficient of the squared term: Divide each side by '0.484'. -0.007438016529 + -2.229917355x + x2 = 0 Move the constant term to the right: Add '0.007438016529' to each side of the equation. -0.007438016529 + -2.229917355x + 0.007438016529 + x2 = 0 + 0.007438016529 Reorder the terms: -0.007438016529 + 0.007438016529 + -2.229917355x + x2 = 0 + 0.007438016529 Combine like terms: -0.007438016529 + 0.007438016529 = 0.000000000000 0.000000000000 + -2.229917355x + x2 = 0 + 0.007438016529 -2.229917355x + x2 = 0 + 0.007438016529 Combine like terms: 0 + 0.007438016529 = 0.007438016529 -2.229917355x + x2 = 0.007438016529 The x term is -2.229917355x. Take half its coefficient (-1.114958678). Square it (1.243132854) and add it to both sides. Add '1.243132854' to each side of the equation. -2.229917355x + 1.243132854 + x2 = 0.007438016529 + 1.243132854 Reorder the terms: 1.243132854 + -2.229917355x + x2 = 0.007438016529 + 1.243132854 Combine like terms: 0.007438016529 + 1.243132854 = 1.250570870529 1.243132854 + -2.229917355x + x2 = 1.250570870529 Factor a perfect square on the left side: (x + -1.114958678)(x + -1.114958678) = 1.250570870529 Calculate the square root of the right side: 1.118289261 Break this problem into two subproblems by setting (x + -1.114958678) equal to 1.118289261 and -1.118289261.Subproblem 1
x + -1.114958678 = 1.118289261 Simplifying x + -1.114958678 = 1.118289261 Reorder the terms: -1.114958678 + x = 1.118289261 Solving -1.114958678 + x = 1.118289261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.114958678' to each side of the equation. -1.114958678 + 1.114958678 + x = 1.118289261 + 1.114958678 Combine like terms: -1.114958678 + 1.114958678 = 0.000000000 0.000000000 + x = 1.118289261 + 1.114958678 x = 1.118289261 + 1.114958678 Combine like terms: 1.118289261 + 1.114958678 = 2.233247939 x = 2.233247939 Simplifying x = 2.233247939Subproblem 2
x + -1.114958678 = -1.118289261 Simplifying x + -1.114958678 = -1.118289261 Reorder the terms: -1.114958678 + x = -1.118289261 Solving -1.114958678 + x = -1.118289261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.114958678' to each side of the equation. -1.114958678 + 1.114958678 + x = -1.118289261 + 1.114958678 Combine like terms: -1.114958678 + 1.114958678 = 0.000000000 0.000000000 + x = -1.118289261 + 1.114958678 x = -1.118289261 + 1.114958678 Combine like terms: -1.118289261 + 1.114958678 = -0.003330583 x = -0.003330583 Simplifying x = -0.003330583Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.233247939, -0.003330583}
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