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Simplifying 3x2 + -0.5x + -104.5 = 0 Reorder the terms: -104.5 + -0.5x + 3x2 = 0 Solving -104.5 + -0.5x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -34.83333333 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '34.83333333' to each side of the equation. -34.83333333 + -0.1666666667x + 34.83333333 + x2 = 0 + 34.83333333 Reorder the terms: -34.83333333 + 34.83333333 + -0.1666666667x + x2 = 0 + 34.83333333 Combine like terms: -34.83333333 + 34.83333333 = 0.00000000 0.00000000 + -0.1666666667x + x2 = 0 + 34.83333333 -0.1666666667x + x2 = 0 + 34.83333333 Combine like terms: 0 + 34.83333333 = 34.83333333 -0.1666666667x + x2 = 34.83333333 The x term is -0.1666666667x. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667x + 0.006944444447 + x2 = 34.83333333 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 34.83333333 + 0.006944444447 Combine like terms: 34.83333333 + 0.006944444447 = 34.840277774447 0.006944444447 + -0.1666666667x + x2 = 34.840277774447 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 34.840277774447 Calculate the square root of the right side: 5.902565355 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 5.902565355 and -5.902565355.Subproblem 1
x + -0.08333333335 = 5.902565355 Simplifying x + -0.08333333335 = 5.902565355 Reorder the terms: -0.08333333335 + x = 5.902565355 Solving -0.08333333335 + x = 5.902565355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 5.902565355 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 5.902565355 + 0.08333333335 x = 5.902565355 + 0.08333333335 Combine like terms: 5.902565355 + 0.08333333335 = 5.98589868835 x = 5.98589868835 Simplifying x = 5.98589868835Subproblem 2
x + -0.08333333335 = -5.902565355 Simplifying x + -0.08333333335 = -5.902565355 Reorder the terms: -0.08333333335 + x = -5.902565355 Solving -0.08333333335 + x = -5.902565355 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -5.902565355 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -5.902565355 + 0.08333333335 x = -5.902565355 + 0.08333333335 Combine like terms: -5.902565355 + 0.08333333335 = -5.81923202165 x = -5.81923202165 Simplifying x = -5.81923202165Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.98589868835, -5.81923202165}
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