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Simplifying 121 = -0.2x2 + 10x + 1 Reorder the terms: 121 = 1 + 10x + -0.2x2 Solving 121 = 1 + 10x + -0.2x2 Solving for variable 'x'. Combine like terms: 121 + -1 = 120 120 + -10x + 0.2x2 = 1 + 10x + -0.2x2 + -1 + -10x + 0.2x2 Reorder the terms: 120 + -10x + 0.2x2 = 1 + -1 + 10x + -10x + -0.2x2 + 0.2x2 Combine like terms: 1 + -1 = 0 120 + -10x + 0.2x2 = 0 + 10x + -10x + -0.2x2 + 0.2x2 120 + -10x + 0.2x2 = 10x + -10x + -0.2x2 + 0.2x2 Combine like terms: 10x + -10x = 0 120 + -10x + 0.2x2 = 0 + -0.2x2 + 0.2x2 120 + -10x + 0.2x2 = -0.2x2 + 0.2x2 Combine like terms: -0.2x2 + 0.2x2 = 0.0 120 + -10x + 0.2x2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 600 + -50x + x2 = 0 Move the constant term to the right: Add '-600' to each side of the equation. 600 + -50x + -600 + x2 = 0 + -600 Reorder the terms: 600 + -600 + -50x + x2 = 0 + -600 Combine like terms: 600 + -600 = 0 0 + -50x + x2 = 0 + -600 -50x + x2 = 0 + -600 Combine like terms: 0 + -600 = -600 -50x + x2 = -600 The x term is -50x. Take half its coefficient (-25). Square it (625) and add it to both sides. Add '625' to each side of the equation. -50x + 625 + x2 = -600 + 625 Reorder the terms: 625 + -50x + x2 = -600 + 625 Combine like terms: -600 + 625 = 25 625 + -50x + x2 = 25 Factor a perfect square on the left side: (x + -25)(x + -25) = 25 Calculate the square root of the right side: 5 Break this problem into two subproblems by setting (x + -25) equal to 5 and -5.Subproblem 1
x + -25 = 5 Simplifying x + -25 = 5 Reorder the terms: -25 + x = 5 Solving -25 + x = 5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = 5 + 25 Combine like terms: -25 + 25 = 0 0 + x = 5 + 25 x = 5 + 25 Combine like terms: 5 + 25 = 30 x = 30 Simplifying x = 30Subproblem 2
x + -25 = -5 Simplifying x + -25 = -5 Reorder the terms: -25 + x = -5 Solving -25 + x = -5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + x = -5 + 25 Combine like terms: -25 + 25 = 0 0 + x = -5 + 25 x = -5 + 25 Combine like terms: -5 + 25 = 20 x = 20 Simplifying x = 20Solution
The solution to the problem is based on the solutions from the subproblems. x = {30, 20}
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