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Simplifying 1.8x + -0.001x2 = 0.3x + 60 Reorder the terms: 1.8x + -0.001x2 = 60 + 0.3x Solving 1.8x + -0.001x2 = 60 + 0.3x Solving for variable 'x'. Reorder the terms: -60 + 1.8x + -0.3x + -0.001x2 = 60 + 0.3x + -60 + -0.3x Combine like terms: 1.8x + -0.3x = 1.5x -60 + 1.5x + -0.001x2 = 60 + 0.3x + -60 + -0.3x Reorder the terms: -60 + 1.5x + -0.001x2 = 60 + -60 + 0.3x + -0.3x Combine like terms: 60 + -60 = 0 -60 + 1.5x + -0.001x2 = 0 + 0.3x + -0.3x -60 + 1.5x + -0.001x2 = 0.3x + -0.3x Combine like terms: 0.3x + -0.3x = 0.0 -60 + 1.5x + -0.001x2 = 0.0 Begin completing the square. Divide all terms by -0.001 the coefficient of the squared term: Divide each side by '-0.001'. 60000 + -1500x + x2 = 0 Move the constant term to the right: Add '-60000' to each side of the equation. 60000 + -1500x + -60000 + x2 = 0 + -60000 Reorder the terms: 60000 + -60000 + -1500x + x2 = 0 + -60000 Combine like terms: 60000 + -60000 = 0 0 + -1500x + x2 = 0 + -60000 -1500x + x2 = 0 + -60000 Combine like terms: 0 + -60000 = -60000 -1500x + x2 = -60000 The x term is -1500x. Take half its coefficient (-750). Square it (562500) and add it to both sides. Add '562500' to each side of the equation. -1500x + 562500 + x2 = -60000 + 562500 Reorder the terms: 562500 + -1500x + x2 = -60000 + 562500 Combine like terms: -60000 + 562500 = 502500 562500 + -1500x + x2 = 502500 Factor a perfect square on the left side: (x + -750)(x + -750) = 502500 Calculate the square root of the right side: 708.872343938 Break this problem into two subproblems by setting (x + -750) equal to 708.872343938 and -708.872343938.Subproblem 1
x + -750 = 708.872343938 Simplifying x + -750 = 708.872343938 Reorder the terms: -750 + x = 708.872343938 Solving -750 + x = 708.872343938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '750' to each side of the equation. -750 + 750 + x = 708.872343938 + 750 Combine like terms: -750 + 750 = 0 0 + x = 708.872343938 + 750 x = 708.872343938 + 750 Combine like terms: 708.872343938 + 750 = 1458.872343938 x = 1458.872343938 Simplifying x = 1458.872343938Subproblem 2
x + -750 = -708.872343938 Simplifying x + -750 = -708.872343938 Reorder the terms: -750 + x = -708.872343938 Solving -750 + x = -708.872343938 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '750' to each side of the equation. -750 + 750 + x = -708.872343938 + 750 Combine like terms: -750 + 750 = 0 0 + x = -708.872343938 + 750 x = -708.872343938 + 750 Combine like terms: -708.872343938 + 750 = 41.127656062 x = 41.127656062 Simplifying x = 41.127656062Solution
The solution to the problem is based on the solutions from the subproblems. x = {1458.872343938, 41.127656062}
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