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Simplifying 180 = 16x + -0.1x2 + -100 Reorder the terms: 180 = -100 + 16x + -0.1x2 Solving 180 = -100 + 16x + -0.1x2 Solving for variable 'x'. Combine like terms: 180 + 100 = 280 280 + -16x + 0.1x2 = -100 + 16x + -0.1x2 + 100 + -16x + 0.1x2 Reorder the terms: 280 + -16x + 0.1x2 = -100 + 100 + 16x + -16x + -0.1x2 + 0.1x2 Combine like terms: -100 + 100 = 0 280 + -16x + 0.1x2 = 0 + 16x + -16x + -0.1x2 + 0.1x2 280 + -16x + 0.1x2 = 16x + -16x + -0.1x2 + 0.1x2 Combine like terms: 16x + -16x = 0 280 + -16x + 0.1x2 = 0 + -0.1x2 + 0.1x2 280 + -16x + 0.1x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 280 + -16x + 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'. 2800 + -160x + x2 = 0 Move the constant term to the right: Add '-2800' to each side of the equation. 2800 + -160x + -2800 + x2 = 0 + -2800 Reorder the terms: 2800 + -2800 + -160x + x2 = 0 + -2800 Combine like terms: 2800 + -2800 = 0 0 + -160x + x2 = 0 + -2800 -160x + x2 = 0 + -2800 Combine like terms: 0 + -2800 = -2800 -160x + x2 = -2800 The x term is -160x. Take half its coefficient (-80). Square it (6400) and add it to both sides. Add '6400' to each side of the equation. -160x + 6400 + x2 = -2800 + 6400 Reorder the terms: 6400 + -160x + x2 = -2800 + 6400 Combine like terms: -2800 + 6400 = 3600 6400 + -160x + x2 = 3600 Factor a perfect square on the left side: (x + -80)(x + -80) = 3600 Calculate the square root of the right side: 60 Break this problem into two subproblems by setting (x + -80) equal to 60 and -60.Subproblem 1
x + -80 = 60 Simplifying x + -80 = 60 Reorder the terms: -80 + x = 60 Solving -80 + x = 60 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = 60 + 80 Combine like terms: -80 + 80 = 0 0 + x = 60 + 80 x = 60 + 80 Combine like terms: 60 + 80 = 140 x = 140 Simplifying x = 140Subproblem 2
x + -80 = -60 Simplifying x + -80 = -60 Reorder the terms: -80 + x = -60 Solving -80 + x = -60 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '80' to each side of the equation. -80 + 80 + x = -60 + 80 Combine like terms: -80 + 80 = 0 0 + x = -60 + 80 x = -60 + 80 Combine like terms: -60 + 80 = 20 x = 20 Simplifying x = 20Solution
The solution to the problem is based on the solutions from the subproblems. x = {140, 20}
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