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Simplifying x + (x * 0.15x) = 375 Reorder the terms for easier multiplication: x + (0.15x * x) = 375 Multiply x * x x + (0.15x2) = 375 Solving x + (0.15x2) = 375 Solving for variable 'x'. Reorder the terms: -375 + x + (0.15x2) = 375 + -375 Combine like terms: 375 + -375 = 0 -375 + x + (0.15x2) = 0 Begin completing the square. Divide all terms by 0.15 the coefficient of the squared term: Divide each side by '0.15'. -2500 + 6.666666667x + x2 = 0 Move the constant term to the right: Add '2500' to each side of the equation. -2500 + 6.666666667x + 2500 + x2 = 0 + 2500 Reorder the terms: -2500 + 2500 + 6.666666667x + x2 = 0 + 2500 Combine like terms: -2500 + 2500 = 0 0 + 6.666666667x + x2 = 0 + 2500 6.666666667x + x2 = 0 + 2500 Combine like terms: 0 + 2500 = 2500 6.666666667x + x2 = 2500 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 6.666666667x + 0.25 + x2 = 2500 + 0.25 Reorder the terms: 0.25 + 6.666666667x + x2 = 2500 + 0.25 Combine like terms: 2500 + 0.25 = 2500.25 0.25 + 6.666666667x + x2 = 2500.25 Factor a perfect square on the left side: ((x) + 0.5)((x) + 0.5) = 2500.25 Calculate the square root of the right side: 50.002499938 Break this problem into two subproblems by setting ((x) + 0.5) equal to 50.002499938 and -50.002499938.Subproblem 1
(x) + 0.5 = 50.002499938 Simplifying (x) + 0.5 = 50.002499938 x + 0.5 = 50.002499938 Reorder the terms: 0.5 + x = 50.002499938 Solving 0.5 + x = 50.002499938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 50.002499938 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 50.002499938 + -0.5 x = 50.002499938 + -0.5 Combine like terms: 50.002499938 + -0.5 = 49.502499938 x = 49.502499938 Simplifying x = 49.502499938Subproblem 2
(x) + 0.5 = -50.002499938 Simplifying (x) + 0.5 = -50.002499938 x + 0.5 = -50.002499938 Reorder the terms: 0.5 + x = -50.002499938 Solving 0.5 + x = -50.002499938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -50.002499938 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -50.002499938 + -0.5 x = -50.002499938 + -0.5 Combine like terms: -50.002499938 + -0.5 = -50.502499938 x = -50.502499938 Simplifying x = -50.502499938Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.502499938, -50.502499938}
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