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Simplifying 20x + -1x2 = 0.75 Solving 20x + -1x2 = 0.75 Solving for variable 'x'. Reorder the terms: -0.75 + 20x + -1x2 = 0.75 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 -0.75 + 20x + -1x2 = 0.00 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 0.75 + -20x + x2 = 0.00 Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -20x + -0.75 + x2 = 0.00 + -0.75 Reorder the terms: 0.75 + -0.75 + -20x + x2 = 0.00 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -20x + x2 = 0.00 + -0.75 -20x + x2 = 0.00 + -0.75 Combine like terms: 0.00 + -0.75 = -0.75 -20x + x2 = -0.75 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -0.75 + 100 Reorder the terms: 100 + -20x + x2 = -0.75 + 100 Combine like terms: -0.75 + 100 = 99.25 100 + -20x + x2 = 99.25 Factor a perfect square on the left side: (x + -10)(x + -10) = 99.25 Calculate the square root of the right side: 9.962429423 Break this problem into two subproblems by setting (x + -10) equal to 9.962429423 and -9.962429423.Subproblem 1
x + -10 = 9.962429423 Simplifying x + -10 = 9.962429423 Reorder the terms: -10 + x = 9.962429423 Solving -10 + x = 9.962429423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 9.962429423 + 10 Combine like terms: -10 + 10 = 0 0 + x = 9.962429423 + 10 x = 9.962429423 + 10 Combine like terms: 9.962429423 + 10 = 19.962429423 x = 19.962429423 Simplifying x = 19.962429423Subproblem 2
x + -10 = -9.962429423 Simplifying x + -10 = -9.962429423 Reorder the terms: -10 + x = -9.962429423 Solving -10 + x = -9.962429423 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -9.962429423 + 10 Combine like terms: -10 + 10 = 0 0 + x = -9.962429423 + 10 x = -9.962429423 + 10 Combine like terms: -9.962429423 + 10 = 0.037570577 x = 0.037570577 Simplifying x = 0.037570577Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.962429423, 0.037570577}
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