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Simplifying x = 1500 + 220x + -5x2 Solving x = 1500 + 220x + -5x2 Solving for variable 'x'. Reorder the terms: -1500 + x + -220x + 5x2 = 1500 + 220x + -5x2 + -1500 + -220x + 5x2 Combine like terms: x + -220x = -219x -1500 + -219x + 5x2 = 1500 + 220x + -5x2 + -1500 + -220x + 5x2 Reorder the terms: -1500 + -219x + 5x2 = 1500 + -1500 + 220x + -220x + -5x2 + 5x2 Combine like terms: 1500 + -1500 = 0 -1500 + -219x + 5x2 = 0 + 220x + -220x + -5x2 + 5x2 -1500 + -219x + 5x2 = 220x + -220x + -5x2 + 5x2 Combine like terms: 220x + -220x = 0 -1500 + -219x + 5x2 = 0 + -5x2 + 5x2 -1500 + -219x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -1500 + -219x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -300 + -43.8x + x2 = 0 Move the constant term to the right: Add '300' to each side of the equation. -300 + -43.8x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + -43.8x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + -43.8x + x2 = 0 + 300 -43.8x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 -43.8x + x2 = 300 The x term is -43.8x. Take half its coefficient (-21.9). Square it (479.61) and add it to both sides. Add '479.61' to each side of the equation. -43.8x + 479.61 + x2 = 300 + 479.61 Reorder the terms: 479.61 + -43.8x + x2 = 300 + 479.61 Combine like terms: 300 + 479.61 = 779.61 479.61 + -43.8x + x2 = 779.61 Factor a perfect square on the left side: (x + -21.9)(x + -21.9) = 779.61 Calculate the square root of the right side: 27.921497095 Break this problem into two subproblems by setting (x + -21.9) equal to 27.921497095 and -27.921497095.Subproblem 1
x + -21.9 = 27.921497095 Simplifying x + -21.9 = 27.921497095 Reorder the terms: -21.9 + x = 27.921497095 Solving -21.9 + x = 27.921497095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21.9' to each side of the equation. -21.9 + 21.9 + x = 27.921497095 + 21.9 Combine like terms: -21.9 + 21.9 = 0.0 0.0 + x = 27.921497095 + 21.9 x = 27.921497095 + 21.9 Combine like terms: 27.921497095 + 21.9 = 49.821497095 x = 49.821497095 Simplifying x = 49.821497095Subproblem 2
x + -21.9 = -27.921497095 Simplifying x + -21.9 = -27.921497095 Reorder the terms: -21.9 + x = -27.921497095 Solving -21.9 + x = -27.921497095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '21.9' to each side of the equation. -21.9 + 21.9 + x = -27.921497095 + 21.9 Combine like terms: -21.9 + 21.9 = 0.0 0.0 + x = -27.921497095 + 21.9 x = -27.921497095 + 21.9 Combine like terms: -27.921497095 + 21.9 = -6.021497095 x = -6.021497095 Simplifying x = -6.021497095Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.821497095, -6.021497095}
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