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Simplifying 150x = 3000 + 9x + 0.1x2 Solving 150x = 3000 + 9x + 0.1x2 Solving for variable 'x'. Reorder the terms: -3000 + 150x + -9x + -0.1x2 = 3000 + 9x + 0.1x2 + -3000 + -9x + -0.1x2 Combine like terms: 150x + -9x = 141x -3000 + 141x + -0.1x2 = 3000 + 9x + 0.1x2 + -3000 + -9x + -0.1x2 Reorder the terms: -3000 + 141x + -0.1x2 = 3000 + -3000 + 9x + -9x + 0.1x2 + -0.1x2 Combine like terms: 3000 + -3000 = 0 -3000 + 141x + -0.1x2 = 0 + 9x + -9x + 0.1x2 + -0.1x2 -3000 + 141x + -0.1x2 = 9x + -9x + 0.1x2 + -0.1x2 Combine like terms: 9x + -9x = 0 -3000 + 141x + -0.1x2 = 0 + 0.1x2 + -0.1x2 -3000 + 141x + -0.1x2 = 0.1x2 + -0.1x2 Combine like terms: 0.1x2 + -0.1x2 = 0.0 -3000 + 141x + -0.1x2 = 0.0 Begin completing the square. Divide all terms by -0.1 the coefficient of the squared term: Divide each side by '-0.1'. 30000 + -1410x + x2 = 0 Move the constant term to the right: Add '-30000' to each side of the equation. 30000 + -1410x + -30000 + x2 = 0 + -30000 Reorder the terms: 30000 + -30000 + -1410x + x2 = 0 + -30000 Combine like terms: 30000 + -30000 = 0 0 + -1410x + x2 = 0 + -30000 -1410x + x2 = 0 + -30000 Combine like terms: 0 + -30000 = -30000 -1410x + x2 = -30000 The x term is -1410x. Take half its coefficient (-705). Square it (497025) and add it to both sides. Add '497025' to each side of the equation. -1410x + 497025 + x2 = -30000 + 497025 Reorder the terms: 497025 + -1410x + x2 = -30000 + 497025 Combine like terms: -30000 + 497025 = 467025 497025 + -1410x + x2 = 467025 Factor a perfect square on the left side: (x + -705)(x + -705) = 467025 Calculate the square root of the right side: 683.392273881 Break this problem into two subproblems by setting (x + -705) equal to 683.392273881 and -683.392273881.Subproblem 1
x + -705 = 683.392273881 Simplifying x + -705 = 683.392273881 Reorder the terms: -705 + x = 683.392273881 Solving -705 + x = 683.392273881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '705' to each side of the equation. -705 + 705 + x = 683.392273881 + 705 Combine like terms: -705 + 705 = 0 0 + x = 683.392273881 + 705 x = 683.392273881 + 705 Combine like terms: 683.392273881 + 705 = 1388.392273881 x = 1388.392273881 Simplifying x = 1388.392273881Subproblem 2
x + -705 = -683.392273881 Simplifying x + -705 = -683.392273881 Reorder the terms: -705 + x = -683.392273881 Solving -705 + x = -683.392273881 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '705' to each side of the equation. -705 + 705 + x = -683.392273881 + 705 Combine like terms: -705 + 705 = 0 0 + x = -683.392273881 + 705 x = -683.392273881 + 705 Combine like terms: -683.392273881 + 705 = 21.607726119 x = 21.607726119 Simplifying x = 21.607726119Solution
The solution to the problem is based on the solutions from the subproblems. x = {1388.392273881, 21.607726119}
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