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Simplifying 0 = -0.01x2 + -0.1x + 20 Reorder the terms: 0 = 20 + -0.1x + -0.01x2 Solving 0 = 20 + -0.1x + -0.01x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + 0.1x + 0.01x2 = 20 + -0.1x + -0.01x2 + -20 + 0.1x + 0.01x2 Reorder the terms: -20 + 0.1x + 0.01x2 = 20 + -20 + -0.1x + 0.1x + -0.01x2 + 0.01x2 Combine like terms: 20 + -20 = 0 -20 + 0.1x + 0.01x2 = 0 + -0.1x + 0.1x + -0.01x2 + 0.01x2 -20 + 0.1x + 0.01x2 = -0.1x + 0.1x + -0.01x2 + 0.01x2 Combine like terms: -0.1x + 0.1x = 0.0 -20 + 0.1x + 0.01x2 = 0.0 + -0.01x2 + 0.01x2 -20 + 0.1x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 -20 + 0.1x + 0.01x2 = 0.00 Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. -2000 + 10x + x2 = 0 Move the constant term to the right: Add '2000' to each side of the equation. -2000 + 10x + 2000 + x2 = 0 + 2000 Reorder the terms: -2000 + 2000 + 10x + x2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + 10x + x2 = 0 + 2000 10x + x2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 10x + x2 = 2000 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = 2000 + 25 Reorder the terms: 25 + 10x + x2 = 2000 + 25 Combine like terms: 2000 + 25 = 2025 25 + 10x + x2 = 2025 Factor a perfect square on the left side: (x + 5)(x + 5) = 2025 Calculate the square root of the right side: 45 Break this problem into two subproblems by setting (x + 5) equal to 45 and -45.Subproblem 1
x + 5 = 45 Simplifying x + 5 = 45 Reorder the terms: 5 + x = 45 Solving 5 + x = 45 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 45 + -5 Combine like terms: 5 + -5 = 0 0 + x = 45 + -5 x = 45 + -5 Combine like terms: 45 + -5 = 40 x = 40 Simplifying x = 40Subproblem 2
x + 5 = -45 Simplifying x + 5 = -45 Reorder the terms: 5 + x = -45 Solving 5 + x = -45 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -45 + -5 Combine like terms: 5 + -5 = 0 0 + x = -45 + -5 x = -45 + -5 Combine like terms: -45 + -5 = -50 x = -50 Simplifying x = -50Solution
The solution to the problem is based on the solutions from the subproblems. x = {40, -50}
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