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Simplifying 58x + -0.3x2 = 11x + 12 Reorder the terms: 58x + -0.3x2 = 12 + 11x Solving 58x + -0.3x2 = 12 + 11x Solving for variable 'x'. Reorder the terms: -12 + 58x + -11x + -0.3x2 = 12 + 11x + -12 + -11x Combine like terms: 58x + -11x = 47x -12 + 47x + -0.3x2 = 12 + 11x + -12 + -11x Reorder the terms: -12 + 47x + -0.3x2 = 12 + -12 + 11x + -11x Combine like terms: 12 + -12 = 0 -12 + 47x + -0.3x2 = 0 + 11x + -11x -12 + 47x + -0.3x2 = 11x + -11x Combine like terms: 11x + -11x = 0 -12 + 47x + -0.3x2 = 0 Begin completing the square. Divide all terms by -0.3 the coefficient of the squared term: Divide each side by '-0.3'. 40 + -156.6666667x + x2 = 0 Move the constant term to the right: Add '-40' to each side of the equation. 40 + -156.6666667x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -156.6666667x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -156.6666667x + x2 = 0 + -40 -156.6666667x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -156.6666667x + x2 = -40 The x term is -156.6666667x. Take half its coefficient (-78.33333335). Square it (6136.111114) and add it to both sides. Add '6136.111114' to each side of the equation. -156.6666667x + 6136.111114 + x2 = -40 + 6136.111114 Reorder the terms: 6136.111114 + -156.6666667x + x2 = -40 + 6136.111114 Combine like terms: -40 + 6136.111114 = 6096.111114 6136.111114 + -156.6666667x + x2 = 6096.111114 Factor a perfect square on the left side: (x + -78.33333335)(x + -78.33333335) = 6096.111114 Calculate the square root of the right side: 78.077596748 Break this problem into two subproblems by setting (x + -78.33333335) equal to 78.077596748 and -78.077596748.Subproblem 1
x + -78.33333335 = 78.077596748 Simplifying x + -78.33333335 = 78.077596748 Reorder the terms: -78.33333335 + x = 78.077596748 Solving -78.33333335 + x = 78.077596748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '78.33333335' to each side of the equation. -78.33333335 + 78.33333335 + x = 78.077596748 + 78.33333335 Combine like terms: -78.33333335 + 78.33333335 = 0.00000000 0.00000000 + x = 78.077596748 + 78.33333335 x = 78.077596748 + 78.33333335 Combine like terms: 78.077596748 + 78.33333335 = 156.410930098 x = 156.410930098 Simplifying x = 156.410930098Subproblem 2
x + -78.33333335 = -78.077596748 Simplifying x + -78.33333335 = -78.077596748 Reorder the terms: -78.33333335 + x = -78.077596748 Solving -78.33333335 + x = -78.077596748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '78.33333335' to each side of the equation. -78.33333335 + 78.33333335 + x = -78.077596748 + 78.33333335 Combine like terms: -78.33333335 + 78.33333335 = 0.00000000 0.00000000 + x = -78.077596748 + 78.33333335 x = -78.077596748 + 78.33333335 Combine like terms: -78.077596748 + 78.33333335 = 0.255736602 x = 0.255736602 Simplifying x = 0.255736602Solution
The solution to the problem is based on the solutions from the subproblems. x = {156.410930098, 0.255736602}
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