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Simplifying 0.01x(5 + -0.2x) = 0.75 + 0.198x (5 * 0.01x + -0.2x * 0.01x) = 0.75 + 0.198x (0.05x + -0.002x2) = 0.75 + 0.198x Solving 0.05x + -0.002x2 = 0.75 + 0.198x Solving for variable 'x'. Reorder the terms: -0.75 + 0.05x + -0.198x + -0.002x2 = 0.75 + 0.198x + -0.75 + -0.198x Combine like terms: 0.05x + -0.198x = -0.148x -0.75 + -0.148x + -0.002x2 = 0.75 + 0.198x + -0.75 + -0.198x Reorder the terms: -0.75 + -0.148x + -0.002x2 = 0.75 + -0.75 + 0.198x + -0.198x Combine like terms: 0.75 + -0.75 = 0.00 -0.75 + -0.148x + -0.002x2 = 0.00 + 0.198x + -0.198x -0.75 + -0.148x + -0.002x2 = 0.198x + -0.198x Combine like terms: 0.198x + -0.198x = 0.000 -0.75 + -0.148x + -0.002x2 = 0.000 Begin completing the square. Divide all terms by -0.002 the coefficient of the squared term: Divide each side by '-0.002'. 375 + 74x + x2 = 0 Move the constant term to the right: Add '-375' to each side of the equation. 375 + 74x + -375 + x2 = 0 + -375 Reorder the terms: 375 + -375 + 74x + x2 = 0 + -375 Combine like terms: 375 + -375 = 0 0 + 74x + x2 = 0 + -375 74x + x2 = 0 + -375 Combine like terms: 0 + -375 = -375 74x + x2 = -375 The x term is 74x. Take half its coefficient (37). Square it (1369) and add it to both sides. Add '1369' to each side of the equation. 74x + 1369 + x2 = -375 + 1369 Reorder the terms: 1369 + 74x + x2 = -375 + 1369 Combine like terms: -375 + 1369 = 994 1369 + 74x + x2 = 994 Factor a perfect square on the left side: (x + 37)(x + 37) = 994 Calculate the square root of the right side: 31.527765541 Break this problem into two subproblems by setting (x + 37) equal to 31.527765541 and -31.527765541.Subproblem 1
x + 37 = 31.527765541 Simplifying x + 37 = 31.527765541 Reorder the terms: 37 + x = 31.527765541 Solving 37 + x = 31.527765541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-37' to each side of the equation. 37 + -37 + x = 31.527765541 + -37 Combine like terms: 37 + -37 = 0 0 + x = 31.527765541 + -37 x = 31.527765541 + -37 Combine like terms: 31.527765541 + -37 = -5.472234459 x = -5.472234459 Simplifying x = -5.472234459Subproblem 2
x + 37 = -31.527765541 Simplifying x + 37 = -31.527765541 Reorder the terms: 37 + x = -31.527765541 Solving 37 + x = -31.527765541 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-37' to each side of the equation. 37 + -37 + x = -31.527765541 + -37 Combine like terms: 37 + -37 = 0 0 + x = -31.527765541 + -37 x = -31.527765541 + -37 Combine like terms: -31.527765541 + -37 = -68.527765541 x = -68.527765541 Simplifying x = -68.527765541Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.472234459, -68.527765541}
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