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Simplifying x = -0.01x2 + -0.1x + 44 Reorder the terms: x = 44 + -0.1x + -0.01x2 Solving x = 44 + -0.1x + -0.01x2 Solving for variable 'x'. Reorder the terms: -44 + x + 0.1x + 0.01x2 = 44 + -0.1x + -0.01x2 + -44 + 0.1x + 0.01x2 Combine like terms: x + 0.1x = 1.1x -44 + 1.1x + 0.01x2 = 44 + -0.1x + -0.01x2 + -44 + 0.1x + 0.01x2 Reorder the terms: -44 + 1.1x + 0.01x2 = 44 + -44 + -0.1x + 0.1x + -0.01x2 + 0.01x2 Combine like terms: 44 + -44 = 0 -44 + 1.1x + 0.01x2 = 0 + -0.1x + 0.1x + -0.01x2 + 0.01x2 -44 + 1.1x + 0.01x2 = -0.1x + 0.1x + -0.01x2 + 0.01x2 Combine like terms: -0.1x + 0.1x = 0.0 -44 + 1.1x + 0.01x2 = 0.0 + -0.01x2 + 0.01x2 -44 + 1.1x + 0.01x2 = -0.01x2 + 0.01x2 Combine like terms: -0.01x2 + 0.01x2 = 0.00 -44 + 1.1x + 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'. -4400 + 110x + x2 = 0 Move the constant term to the right: Add '4400' to each side of the equation. -4400 + 110x + 4400 + x2 = 0 + 4400 Reorder the terms: -4400 + 4400 + 110x + x2 = 0 + 4400 Combine like terms: -4400 + 4400 = 0 0 + 110x + x2 = 0 + 4400 110x + x2 = 0 + 4400 Combine like terms: 0 + 4400 = 4400 110x + x2 = 4400 The x term is 110x. Take half its coefficient (55). Square it (3025) and add it to both sides. Add '3025' to each side of the equation. 110x + 3025 + x2 = 4400 + 3025 Reorder the terms: 3025 + 110x + x2 = 4400 + 3025 Combine like terms: 4400 + 3025 = 7425 3025 + 110x + x2 = 7425 Factor a perfect square on the left side: (x + 55)(x + 55) = 7425 Calculate the square root of the right side: 86.168439698 Break this problem into two subproblems by setting (x + 55) equal to 86.168439698 and -86.168439698.Subproblem 1
x + 55 = 86.168439698 Simplifying x + 55 = 86.168439698 Reorder the terms: 55 + x = 86.168439698 Solving 55 + x = 86.168439698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-55' to each side of the equation. 55 + -55 + x = 86.168439698 + -55 Combine like terms: 55 + -55 = 0 0 + x = 86.168439698 + -55 x = 86.168439698 + -55 Combine like terms: 86.168439698 + -55 = 31.168439698 x = 31.168439698 Simplifying x = 31.168439698Subproblem 2
x + 55 = -86.168439698 Simplifying x + 55 = -86.168439698 Reorder the terms: 55 + x = -86.168439698 Solving 55 + x = -86.168439698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-55' to each side of the equation. 55 + -55 + x = -86.168439698 + -55 Combine like terms: 55 + -55 = 0 0 + x = -86.168439698 + -55 x = -86.168439698 + -55 Combine like terms: -86.168439698 + -55 = -141.168439698 x = -141.168439698 Simplifying x = -141.168439698Solution
The solution to the problem is based on the solutions from the subproblems. x = {31.168439698, -141.168439698}
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