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Simplifying 2.2x + -0.001x2 = 0.4x + 60 Reorder the terms: 2.2x + -0.001x2 = 60 + 0.4x Solving 2.2x + -0.001x2 = 60 + 0.4x Solving for variable 'x'. Reorder the terms: -60 + 2.2x + -0.4x + -0.001x2 = 60 + 0.4x + -60 + -0.4x Combine like terms: 2.2x + -0.4x = 1.8x -60 + 1.8x + -0.001x2 = 60 + 0.4x + -60 + -0.4x Reorder the terms: -60 + 1.8x + -0.001x2 = 60 + -60 + 0.4x + -0.4x Combine like terms: 60 + -60 = 0 -60 + 1.8x + -0.001x2 = 0 + 0.4x + -0.4x -60 + 1.8x + -0.001x2 = 0.4x + -0.4x Combine like terms: 0.4x + -0.4x = 0.0 -60 + 1.8x + -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 + -1800x + x2 = 0 Move the constant term to the right: Add '-60000' to each side of the equation. 60000 + -1800x + -60000 + x2 = 0 + -60000 Reorder the terms: 60000 + -60000 + -1800x + x2 = 0 + -60000 Combine like terms: 60000 + -60000 = 0 0 + -1800x + x2 = 0 + -60000 -1800x + x2 = 0 + -60000 Combine like terms: 0 + -60000 = -60000 -1800x + x2 = -60000 The x term is -1800x. Take half its coefficient (-900). Square it (810000) and add it to both sides. Add '810000' to each side of the equation. -1800x + 810000 + x2 = -60000 + 810000 Reorder the terms: 810000 + -1800x + x2 = -60000 + 810000 Combine like terms: -60000 + 810000 = 750000 810000 + -1800x + x2 = 750000 Factor a perfect square on the left side: (x + -900)(x + -900) = 750000 Calculate the square root of the right side: 866.025403784 Break this problem into two subproblems by setting (x + -900) equal to 866.025403784 and -866.025403784.Subproblem 1
x + -900 = 866.025403784 Simplifying x + -900 = 866.025403784 Reorder the terms: -900 + x = 866.025403784 Solving -900 + x = 866.025403784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '900' to each side of the equation. -900 + 900 + x = 866.025403784 + 900 Combine like terms: -900 + 900 = 0 0 + x = 866.025403784 + 900 x = 866.025403784 + 900 Combine like terms: 866.025403784 + 900 = 1766.025403784 x = 1766.025403784 Simplifying x = 1766.025403784Subproblem 2
x + -900 = -866.025403784 Simplifying x + -900 = -866.025403784 Reorder the terms: -900 + x = -866.025403784 Solving -900 + x = -866.025403784 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '900' to each side of the equation. -900 + 900 + x = -866.025403784 + 900 Combine like terms: -900 + 900 = 0 0 + x = -866.025403784 + 900 x = -866.025403784 + 900 Combine like terms: -866.025403784 + 900 = 33.974596216 x = 33.974596216 Simplifying x = 33.974596216Solution
The solution to the problem is based on the solutions from the subproblems. x = {1766.025403784, 33.974596216}
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