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Simplifying 40500 + 270x + 150x + x2 = 18400 Combine like terms: 270x + 150x = 420x 40500 + 420x + x2 = 18400 Solving 40500 + 420x + x2 = 18400 Solving for variable 'x'. Reorder the terms: 40500 + -18400 + 420x + x2 = 18400 + -18400 Combine like terms: 40500 + -18400 = 22100 22100 + 420x + x2 = 18400 + -18400 Combine like terms: 18400 + -18400 = 0 22100 + 420x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-22100' to each side of the equation. 22100 + 420x + -22100 + x2 = 0 + -22100 Reorder the terms: 22100 + -22100 + 420x + x2 = 0 + -22100 Combine like terms: 22100 + -22100 = 0 0 + 420x + x2 = 0 + -22100 420x + x2 = 0 + -22100 Combine like terms: 0 + -22100 = -22100 420x + x2 = -22100 The x term is 420x. Take half its coefficient (210). Square it (44100) and add it to both sides. Add '44100' to each side of the equation. 420x + 44100 + x2 = -22100 + 44100 Reorder the terms: 44100 + 420x + x2 = -22100 + 44100 Combine like terms: -22100 + 44100 = 22000 44100 + 420x + x2 = 22000 Factor a perfect square on the left side: (x + 210)(x + 210) = 22000 Calculate the square root of the right side: 148.323969742 Break this problem into two subproblems by setting (x + 210) equal to 148.323969742 and -148.323969742.Subproblem 1
x + 210 = 148.323969742 Simplifying x + 210 = 148.323969742 Reorder the terms: 210 + x = 148.323969742 Solving 210 + x = 148.323969742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-210' to each side of the equation. 210 + -210 + x = 148.323969742 + -210 Combine like terms: 210 + -210 = 0 0 + x = 148.323969742 + -210 x = 148.323969742 + -210 Combine like terms: 148.323969742 + -210 = -61.676030258 x = -61.676030258 Simplifying x = -61.676030258Subproblem 2
x + 210 = -148.323969742 Simplifying x + 210 = -148.323969742 Reorder the terms: 210 + x = -148.323969742 Solving 210 + x = -148.323969742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-210' to each side of the equation. 210 + -210 + x = -148.323969742 + -210 Combine like terms: 210 + -210 = 0 0 + x = -148.323969742 + -210 x = -148.323969742 + -210 Combine like terms: -148.323969742 + -210 = -358.323969742 x = -358.323969742 Simplifying x = -358.323969742Solution
The solution to the problem is based on the solutions from the subproblems. x = {-61.676030258, -358.323969742}
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