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Simplifying 9 = 0.007X2 + 0.003X Reorder the terms: 9 = 0.003X + 0.007X2 Solving 9 = 0.003X + 0.007X2 Solving for variable 'X'. Reorder the terms: 9 + -0.003X + -0.007X2 = 0.003X + -0.003X + 0.007X2 + -0.007X2 Combine like terms: 0.003X + -0.003X = 0.000 9 + -0.003X + -0.007X2 = 0.000 + 0.007X2 + -0.007X2 9 + -0.003X + -0.007X2 = 0.007X2 + -0.007X2 Combine like terms: 0.007X2 + -0.007X2 = 0.000 9 + -0.003X + -0.007X2 = 0.000 Begin completing the square. Divide all terms by -0.007 the coefficient of the squared term: Divide each side by '-0.007'. -1285.714286 + 0.4285714286X + X2 = 0 Move the constant term to the right: Add '1285.714286' to each side of the equation. -1285.714286 + 0.4285714286X + 1285.714286 + X2 = 0 + 1285.714286 Reorder the terms: -1285.714286 + 1285.714286 + 0.4285714286X + X2 = 0 + 1285.714286 Combine like terms: -1285.714286 + 1285.714286 = 0.000000 0.000000 + 0.4285714286X + X2 = 0 + 1285.714286 0.4285714286X + X2 = 0 + 1285.714286 Combine like terms: 0 + 1285.714286 = 1285.714286 0.4285714286X + X2 = 1285.714286 The X term is 0.4285714286X. Take half its coefficient (0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. 0.4285714286X + 0.04591836735 + X2 = 1285.714286 + 0.04591836735 Reorder the terms: 0.04591836735 + 0.4285714286X + X2 = 1285.714286 + 0.04591836735 Combine like terms: 1285.714286 + 0.04591836735 = 1285.76020436735 0.04591836735 + 0.4285714286X + X2 = 1285.76020436735 Factor a perfect square on the left side: (X + 0.2142857143)(X + 0.2142857143) = 1285.76020436735 Calculate the square root of the right side: 35.857498579 Break this problem into two subproblems by setting (X + 0.2142857143) equal to 35.857498579 and -35.857498579.Subproblem 1
X + 0.2142857143 = 35.857498579 Simplifying X + 0.2142857143 = 35.857498579 Reorder the terms: 0.2142857143 + X = 35.857498579 Solving 0.2142857143 + X = 35.857498579 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + X = 35.857498579 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + X = 35.857498579 + -0.2142857143 X = 35.857498579 + -0.2142857143 Combine like terms: 35.857498579 + -0.2142857143 = 35.6432128647 X = 35.6432128647 Simplifying X = 35.6432128647Subproblem 2
X + 0.2142857143 = -35.857498579 Simplifying X + 0.2142857143 = -35.857498579 Reorder the terms: 0.2142857143 + X = -35.857498579 Solving 0.2142857143 + X = -35.857498579 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-0.2142857143' to each side of the equation. 0.2142857143 + -0.2142857143 + X = -35.857498579 + -0.2142857143 Combine like terms: 0.2142857143 + -0.2142857143 = 0.0000000000 0.0000000000 + X = -35.857498579 + -0.2142857143 X = -35.857498579 + -0.2142857143 Combine like terms: -35.857498579 + -0.2142857143 = -36.0717842933 X = -36.0717842933 Simplifying X = -36.0717842933Solution
The solution to the problem is based on the solutions from the subproblems. X = {35.6432128647, -36.0717842933}
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