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Simplifying 0.1(x + 50) * 0.3x = 9 Reorder the terms: 0.1(50 + x) * 0.3x = 9 Reorder the terms for easier multiplication: 0.1 * 0.3x(50 + x) = 9 Multiply 0.1 * 0.3 0.03x(50 + x) = 9 (50 * 0.03x + x * 0.03x) = 9 (1.5x + 0.03x2) = 9 Solving 1.5x + 0.03x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + 1.5x + 0.03x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + 1.5x + 0.03x2 = 0 Begin completing the square. Divide all terms by 0.03 the coefficient of the squared term: Divide each side by '0.03'. -300 + 50x + x2 = 0 Move the constant term to the right: Add '300' to each side of the equation. -300 + 50x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + 50x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 50x + x2 = 0 + 300 50x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 50x + x2 = 300 The x term is 50x. Take half its coefficient (25). Square it (625) and add it to both sides. Add '625' to each side of the equation. 50x + 625 + x2 = 300 + 625 Reorder the terms: 625 + 50x + x2 = 300 + 625 Combine like terms: 300 + 625 = 925 625 + 50x + x2 = 925 Factor a perfect square on the left side: (x + 25)(x + 25) = 925 Calculate the square root of the right side: 30.413812651 Break this problem into two subproblems by setting (x + 25) equal to 30.413812651 and -30.413812651.Subproblem 1
x + 25 = 30.413812651 Simplifying x + 25 = 30.413812651 Reorder the terms: 25 + x = 30.413812651 Solving 25 + x = 30.413812651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = 30.413812651 + -25 Combine like terms: 25 + -25 = 0 0 + x = 30.413812651 + -25 x = 30.413812651 + -25 Combine like terms: 30.413812651 + -25 = 5.413812651 x = 5.413812651 Simplifying x = 5.413812651Subproblem 2
x + 25 = -30.413812651 Simplifying x + 25 = -30.413812651 Reorder the terms: 25 + x = -30.413812651 Solving 25 + x = -30.413812651 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + x = -30.413812651 + -25 Combine like terms: 25 + -25 = 0 0 + x = -30.413812651 + -25 x = -30.413812651 + -25 Combine like terms: -30.413812651 + -25 = -55.413812651 x = -55.413812651 Simplifying x = -55.413812651Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.413812651, -55.413812651}
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