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Simplifying 0.1x2 + -2x + 20 = -0.1x2 + -1x + 40 Reorder the terms: 20 + -2x + 0.1x2 = -0.1x2 + -1x + 40 Reorder the terms: 20 + -2x + 0.1x2 = 40 + -1x + -0.1x2 Solving 20 + -2x + 0.1x2 = 40 + -1x + -0.1x2 Solving for variable 'x'. Reorder the terms: 20 + -40 + -2x + x + 0.1x2 + 0.1x2 = 40 + -1x + -0.1x2 + -40 + x + 0.1x2 Combine like terms: 20 + -40 = -20 -20 + -2x + x + 0.1x2 + 0.1x2 = 40 + -1x + -0.1x2 + -40 + x + 0.1x2 Combine like terms: -2x + x = -1x -20 + -1x + 0.1x2 + 0.1x2 = 40 + -1x + -0.1x2 + -40 + x + 0.1x2 Combine like terms: 0.1x2 + 0.1x2 = 0.2x2 -20 + -1x + 0.2x2 = 40 + -1x + -0.1x2 + -40 + x + 0.1x2 Reorder the terms: -20 + -1x + 0.2x2 = 40 + -40 + -1x + x + -0.1x2 + 0.1x2 Combine like terms: 40 + -40 = 0 -20 + -1x + 0.2x2 = 0 + -1x + x + -0.1x2 + 0.1x2 -20 + -1x + 0.2x2 = -1x + x + -0.1x2 + 0.1x2 Combine like terms: -1x + x = 0 -20 + -1x + 0.2x2 = 0 + -0.1x2 + 0.1x2 -20 + -1x + 0.2x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 -20 + -1x + 0.2x2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. -100 + -5x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -5x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -5x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -5x + x2 = 0 + 100 -5x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -5x + x2 = 100 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 100 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 100 + 6.25 Combine like terms: 100 + 6.25 = 106.25 6.25 + -5x + x2 = 106.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 106.25 Calculate the square root of the right side: 10.307764064 Break this problem into two subproblems by setting (x + -2.5) equal to 10.307764064 and -10.307764064.Subproblem 1
x + -2.5 = 10.307764064 Simplifying x + -2.5 = 10.307764064 Reorder the terms: -2.5 + x = 10.307764064 Solving -2.5 + x = 10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 10.307764064 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 10.307764064 + 2.5 x = 10.307764064 + 2.5 Combine like terms: 10.307764064 + 2.5 = 12.807764064 x = 12.807764064 Simplifying x = 12.807764064Subproblem 2
x + -2.5 = -10.307764064 Simplifying x + -2.5 = -10.307764064 Reorder the terms: -2.5 + x = -10.307764064 Solving -2.5 + x = -10.307764064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -10.307764064 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -10.307764064 + 2.5 x = -10.307764064 + 2.5 Combine like terms: -10.307764064 + 2.5 = -7.807764064 x = -7.807764064 Simplifying x = -7.807764064Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.807764064, -7.807764064}
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