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Simplifying 13 + -0.01x2 = 0.1x + 1 Reorder the terms: 13 + -0.01x2 = 1 + 0.1x Solving 13 + -0.01x2 = 1 + 0.1x Solving for variable 'x'. Reorder the terms: 13 + -1 + -0.1x + -0.01x2 = 1 + 0.1x + -1 + -0.1x Combine like terms: 13 + -1 = 12 12 + -0.1x + -0.01x2 = 1 + 0.1x + -1 + -0.1x Reorder the terms: 12 + -0.1x + -0.01x2 = 1 + -1 + 0.1x + -0.1x Combine like terms: 1 + -1 = 0 12 + -0.1x + -0.01x2 = 0 + 0.1x + -0.1x 12 + -0.1x + -0.01x2 = 0.1x + -0.1x Combine like terms: 0.1x + -0.1x = 0.0 12 + -0.1x + -0.01x2 = 0.0 Begin completing the square. Divide all terms by -0.01 the coefficient of the squared term: Divide each side by '-0.01'. -1200 + 10x + x2 = 0 Move the constant term to the right: Add '1200' to each side of the equation. -1200 + 10x + 1200 + x2 = 0 + 1200 Reorder the terms: -1200 + 1200 + 10x + x2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + 10x + x2 = 0 + 1200 10x + x2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 10x + x2 = 1200 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 = 1200 + 25 Reorder the terms: 25 + 10x + x2 = 1200 + 25 Combine like terms: 1200 + 25 = 1225 25 + 10x + x2 = 1225 Factor a perfect square on the left side: (x + 5)(x + 5) = 1225 Calculate the square root of the right side: 35 Break this problem into two subproblems by setting (x + 5) equal to 35 and -35.Subproblem 1
x + 5 = 35 Simplifying x + 5 = 35 Reorder the terms: 5 + x = 35 Solving 5 + x = 35 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 = 35 + -5 Combine like terms: 5 + -5 = 0 0 + x = 35 + -5 x = 35 + -5 Combine like terms: 35 + -5 = 30 x = 30 Simplifying x = 30Subproblem 2
x + 5 = -35 Simplifying x + 5 = -35 Reorder the terms: 5 + x = -35 Solving 5 + x = -35 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 = -35 + -5 Combine like terms: 5 + -5 = 0 0 + x = -35 + -5 x = -35 + -5 Combine like terms: -35 + -5 = -40 x = -40 Simplifying x = -40Solution
The solution to the problem is based on the solutions from the subproblems. x = {30, -40}
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