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Simplifying 33.8x2 + -69.6x + 34.8 = 0 Reorder the terms: 34.8 + -69.6x + 33.8x2 = 0 Solving 34.8 + -69.6x + 33.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 33.8 the coefficient of the squared term: Divide each side by '33.8'. 1.029585799 + -2.059171598x + x2 = 0 Move the constant term to the right: Add '-1.029585799' to each side of the equation. 1.029585799 + -2.059171598x + -1.029585799 + x2 = 0 + -1.029585799 Reorder the terms: 1.029585799 + -1.029585799 + -2.059171598x + x2 = 0 + -1.029585799 Combine like terms: 1.029585799 + -1.029585799 = 0.000000000 0.000000000 + -2.059171598x + x2 = 0 + -1.029585799 -2.059171598x + x2 = 0 + -1.029585799 Combine like terms: 0 + -1.029585799 = -1.029585799 -2.059171598x + x2 = -1.029585799 The x term is -2.059171598x. Take half its coefficient (-1.029585799). Square it (1.060046918) and add it to both sides. Add '1.060046918' to each side of the equation. -2.059171598x + 1.060046918 + x2 = -1.029585799 + 1.060046918 Reorder the terms: 1.060046918 + -2.059171598x + x2 = -1.029585799 + 1.060046918 Combine like terms: -1.029585799 + 1.060046918 = 0.030461119 1.060046918 + -2.059171598x + x2 = 0.030461119 Factor a perfect square on the left side: (x + -1.029585799)(x + -1.029585799) = 0.030461119 Calculate the square root of the right side: 0.17453114 Break this problem into two subproblems by setting (x + -1.029585799) equal to 0.17453114 and -0.17453114.Subproblem 1
x + -1.029585799 = 0.17453114 Simplifying x + -1.029585799 = 0.17453114 Reorder the terms: -1.029585799 + x = 0.17453114 Solving -1.029585799 + x = 0.17453114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.029585799' to each side of the equation. -1.029585799 + 1.029585799 + x = 0.17453114 + 1.029585799 Combine like terms: -1.029585799 + 1.029585799 = 0.000000000 0.000000000 + x = 0.17453114 + 1.029585799 x = 0.17453114 + 1.029585799 Combine like terms: 0.17453114 + 1.029585799 = 1.204116939 x = 1.204116939 Simplifying x = 1.204116939Subproblem 2
x + -1.029585799 = -0.17453114 Simplifying x + -1.029585799 = -0.17453114 Reorder the terms: -1.029585799 + x = -0.17453114 Solving -1.029585799 + x = -0.17453114 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.029585799' to each side of the equation. -1.029585799 + 1.029585799 + x = -0.17453114 + 1.029585799 Combine like terms: -1.029585799 + 1.029585799 = 0.000000000 0.000000000 + x = -0.17453114 + 1.029585799 x = -0.17453114 + 1.029585799 Combine like terms: -0.17453114 + 1.029585799 = 0.855054659 x = 0.855054659 Simplifying x = 0.855054659Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.204116939, 0.855054659}
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