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Simplifying 1 = -0.1x2 + x + 0.1 Reorder the terms: 1 = 0.1 + x + -0.1x2 Solving 1 = 0.1 + x + -0.1x2 Solving for variable 'x'. Combine like terms: 1 + -0.1 = 0.9 0.9 + -1x + 0.1x2 = 0.1 + x + -0.1x2 + -0.1 + -1x + 0.1x2 Reorder the terms: 0.9 + -1x + 0.1x2 = 0.1 + -0.1 + x + -1x + -0.1x2 + 0.1x2 Combine like terms: 0.1 + -0.1 = 0.0 0.9 + -1x + 0.1x2 = 0.0 + x + -1x + -0.1x2 + 0.1x2 0.9 + -1x + 0.1x2 = x + -1x + -0.1x2 + 0.1x2 Combine like terms: x + -1x = 0 0.9 + -1x + 0.1x2 = 0 + -0.1x2 + 0.1x2 0.9 + -1x + 0.1x2 = -0.1x2 + 0.1x2 Combine like terms: -0.1x2 + 0.1x2 = 0.0 0.9 + -1x + 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'. 9 + -10x + x2 = 0 Move the constant term to the right: Add '-9' to each side of the equation. 9 + -10x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + -10x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -10x + x2 = 0 + -9 -10x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 -10x + x2 = -9 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 = -9 + 25 Reorder the terms: 25 + -10x + x2 = -9 + 25 Combine like terms: -9 + 25 = 16 25 + -10x + x2 = 16 Factor a perfect square on the left side: (x + -5)(x + -5) = 16 Calculate the square root of the right side: 4 Break this problem into two subproblems by setting (x + -5) equal to 4 and -4.Subproblem 1
x + -5 = 4 Simplifying x + -5 = 4 Reorder the terms: -5 + x = 4 Solving -5 + x = 4 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 = 4 + 5 Combine like terms: -5 + 5 = 0 0 + x = 4 + 5 x = 4 + 5 Combine like terms: 4 + 5 = 9 x = 9 Simplifying x = 9Subproblem 2
x + -5 = -4 Simplifying x + -5 = -4 Reorder the terms: -5 + x = -4 Solving -5 + x = -4 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 = -4 + 5 Combine like terms: -5 + 5 = 0 0 + x = -4 + 5 x = -4 + 5 Combine like terms: -4 + 5 = 1 x = 1 Simplifying x = 1Solution
The solution to the problem is based on the solutions from the subproblems. x = {9, 1}
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