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Simplifying -5x + 150 = 3 + 0.05x2 Reorder the terms: 150 + -5x = 3 + 0.05x2 Solving 150 + -5x = 3 + 0.05x2 Solving for variable 'x'. Reorder the terms: 150 + -3 + -5x + -0.05x2 = 3 + 0.05x2 + -3 + -0.05x2 Combine like terms: 150 + -3 = 147 147 + -5x + -0.05x2 = 3 + 0.05x2 + -3 + -0.05x2 Reorder the terms: 147 + -5x + -0.05x2 = 3 + -3 + 0.05x2 + -0.05x2 Combine like terms: 3 + -3 = 0 147 + -5x + -0.05x2 = 0 + 0.05x2 + -0.05x2 147 + -5x + -0.05x2 = 0.05x2 + -0.05x2 Combine like terms: 0.05x2 + -0.05x2 = 0.00 147 + -5x + -0.05x2 = 0.00 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -2940 + 100x + x2 = 0 Move the constant term to the right: Add '2940' to each side of the equation. -2940 + 100x + 2940 + x2 = 0 + 2940 Reorder the terms: -2940 + 2940 + 100x + x2 = 0 + 2940 Combine like terms: -2940 + 2940 = 0 0 + 100x + x2 = 0 + 2940 100x + x2 = 0 + 2940 Combine like terms: 0 + 2940 = 2940 100x + x2 = 2940 The x term is 100x. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100x + 2500 + x2 = 2940 + 2500 Reorder the terms: 2500 + 100x + x2 = 2940 + 2500 Combine like terms: 2940 + 2500 = 5440 2500 + 100x + x2 = 5440 Factor a perfect square on the left side: (x + 50)(x + 50) = 5440 Calculate the square root of the right side: 73.756355658 Break this problem into two subproblems by setting (x + 50) equal to 73.756355658 and -73.756355658.Subproblem 1
x + 50 = 73.756355658 Simplifying x + 50 = 73.756355658 Reorder the terms: 50 + x = 73.756355658 Solving 50 + x = 73.756355658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 73.756355658 + -50 Combine like terms: 50 + -50 = 0 0 + x = 73.756355658 + -50 x = 73.756355658 + -50 Combine like terms: 73.756355658 + -50 = 23.756355658 x = 23.756355658 Simplifying x = 23.756355658Subproblem 2
x + 50 = -73.756355658 Simplifying x + 50 = -73.756355658 Reorder the terms: 50 + x = -73.756355658 Solving 50 + x = -73.756355658 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -73.756355658 + -50 Combine like terms: 50 + -50 = 0 0 + x = -73.756355658 + -50 x = -73.756355658 + -50 Combine like terms: -73.756355658 + -50 = -123.756355658 x = -123.756355658 Simplifying x = -123.756355658Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.756355658, -123.756355658}
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