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Simplifying 140 = 10x + -0.1x2 Solving 140 = 10x + -0.1x2 Solving for variable 'x'. Reorder the terms: 140 + -10x + 0.1x2 = 10x + -10x + -0.1x2 + 0.1x2 Combine like terms: 10x + -10x = 0 140 + -10x + 0.1x2 = 0 + -0.1x2 + 0.1x2 140 + -10x + 0.1x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 140 + -10x + 0.1x2 = 0.0 Begin completing the square. Divide all terms by 0.1 the coefficient of the squared term: Divide each side by '0.1'. 1400 + -100x + x2 = 0 Move the constant term to the right: Add '-1400' to each side of the equation. 1400 + -100x + -1400 + x2 = 0 + -1400 Reorder the terms: 1400 + -1400 + -100x + x2 = 0 + -1400 Combine like terms: 1400 + -1400 = 0 0 + -100x + x2 = 0 + -1400 -100x + x2 = 0 + -1400 Combine like terms: 0 + -1400 = -1400 -100x + x2 = -1400 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -1400 + 2500 Reorder the terms: 2500 + -100x + x2 = -1400 + 2500 Combine like terms: -1400 + 2500 = 1100 2500 + -100x + x2 = 1100 Factor a perfect square on the left side: (x + -50)(x + -50) = 1100 Calculate the square root of the right side: 33.166247904 Break this problem into two subproblems by setting (x + -50) equal to 33.166247904 and -33.166247904.Subproblem 1
x + -50 = 33.166247904 Simplifying x + -50 = 33.166247904 Reorder the terms: -50 + x = 33.166247904 Solving -50 + x = 33.166247904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 33.166247904 + 50 Combine like terms: -50 + 50 = 0 0 + x = 33.166247904 + 50 x = 33.166247904 + 50 Combine like terms: 33.166247904 + 50 = 83.166247904 x = 83.166247904 Simplifying x = 83.166247904Subproblem 2
x + -50 = -33.166247904 Simplifying x + -50 = -33.166247904 Reorder the terms: -50 + x = -33.166247904 Solving -50 + x = -33.166247904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -33.166247904 + 50 Combine like terms: -50 + 50 = 0 0 + x = -33.166247904 + 50 x = -33.166247904 + 50 Combine like terms: -33.166247904 + 50 = 16.833752096 x = 16.833752096 Simplifying x = 16.833752096Solution
The solution to the problem is based on the solutions from the subproblems. x = {83.166247904, 16.833752096}
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