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Simplifying 0.485x2 + -1.694x + 0.315 = 98 Reorder the terms: 0.315 + -1.694x + 0.485x2 = 98 Solving 0.315 + -1.694x + 0.485x2 = 98 Solving for variable 'x'. Reorder the terms: 0.315 + -98 + -1.694x + 0.485x2 = 98 + -98 Combine like terms: 0.315 + -98 = -97.685 -97.685 + -1.694x + 0.485x2 = 98 + -98 Combine like terms: 98 + -98 = 0 -97.685 + -1.694x + 0.485x2 = 0 Begin completing the square. Divide all terms by 0.485 the coefficient of the squared term: Divide each side by '0.485'. -201.4123711 + -3.492783505x + x2 = 0 Move the constant term to the right: Add '201.4123711' to each side of the equation. -201.4123711 + -3.492783505x + 201.4123711 + x2 = 0 + 201.4123711 Reorder the terms: -201.4123711 + 201.4123711 + -3.492783505x + x2 = 0 + 201.4123711 Combine like terms: -201.4123711 + 201.4123711 = 0.0000000 0.0000000 + -3.492783505x + x2 = 0 + 201.4123711 -3.492783505x + x2 = 0 + 201.4123711 Combine like terms: 0 + 201.4123711 = 201.4123711 -3.492783505x + x2 = 201.4123711 The x term is -3.492783505x. Take half its coefficient (-1.746391753). Square it (3.049884155) and add it to both sides. Add '3.049884155' to each side of the equation. -3.492783505x + 3.049884155 + x2 = 201.4123711 + 3.049884155 Reorder the terms: 3.049884155 + -3.492783505x + x2 = 201.4123711 + 3.049884155 Combine like terms: 201.4123711 + 3.049884155 = 204.462255255 3.049884155 + -3.492783505x + x2 = 204.462255255 Factor a perfect square on the left side: (x + -1.746391753)(x + -1.746391753) = 204.462255255 Calculate the square root of the right side: 14.299029871 Break this problem into two subproblems by setting (x + -1.746391753) equal to 14.299029871 and -14.299029871.Subproblem 1
x + -1.746391753 = 14.299029871 Simplifying x + -1.746391753 = 14.299029871 Reorder the terms: -1.746391753 + x = 14.299029871 Solving -1.746391753 + x = 14.299029871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.746391753' to each side of the equation. -1.746391753 + 1.746391753 + x = 14.299029871 + 1.746391753 Combine like terms: -1.746391753 + 1.746391753 = 0.000000000 0.000000000 + x = 14.299029871 + 1.746391753 x = 14.299029871 + 1.746391753 Combine like terms: 14.299029871 + 1.746391753 = 16.045421624 x = 16.045421624 Simplifying x = 16.045421624Subproblem 2
x + -1.746391753 = -14.299029871 Simplifying x + -1.746391753 = -14.299029871 Reorder the terms: -1.746391753 + x = -14.299029871 Solving -1.746391753 + x = -14.299029871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.746391753' to each side of the equation. -1.746391753 + 1.746391753 + x = -14.299029871 + 1.746391753 Combine like terms: -1.746391753 + 1.746391753 = 0.000000000 0.000000000 + x = -14.299029871 + 1.746391753 x = -14.299029871 + 1.746391753 Combine like terms: -14.299029871 + 1.746391753 = -12.552638118 x = -12.552638118 Simplifying x = -12.552638118Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.045421624, -12.552638118}
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