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Simplifying 45 = 0.05x2 + x Reorder the terms: 45 = x + 0.05x2 Solving 45 = x + 0.05x2 Solving for variable 'x'. Reorder the terms: 45 + -1x + -0.05x2 = x + -1x + 0.05x2 + -0.05x2 Combine like terms: x + -1x = 0 45 + -1x + -0.05x2 = 0 + 0.05x2 + -0.05x2 45 + -1x + -0.05x2 = 0.05x2 + -0.05x2 Combine like terms: 0.05x2 + -0.05x2 = 0.00 45 + -1x + -0.05x2 = 0.00 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -900 + 20x + x2 = 0 Move the constant term to the right: Add '900' to each side of the equation. -900 + 20x + 900 + x2 = 0 + 900 Reorder the terms: -900 + 900 + 20x + x2 = 0 + 900 Combine like terms: -900 + 900 = 0 0 + 20x + x2 = 0 + 900 20x + x2 = 0 + 900 Combine like terms: 0 + 900 = 900 20x + x2 = 900 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 900 + 100 Reorder the terms: 100 + 20x + x2 = 900 + 100 Combine like terms: 900 + 100 = 1000 100 + 20x + x2 = 1000 Factor a perfect square on the left side: (x + 10)(x + 10) = 1000 Calculate the square root of the right side: 31.622776602 Break this problem into two subproblems by setting (x + 10) equal to 31.622776602 and -31.622776602.Subproblem 1
x + 10 = 31.622776602 Simplifying x + 10 = 31.622776602 Reorder the terms: 10 + x = 31.622776602 Solving 10 + x = 31.622776602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 31.622776602 + -10 Combine like terms: 10 + -10 = 0 0 + x = 31.622776602 + -10 x = 31.622776602 + -10 Combine like terms: 31.622776602 + -10 = 21.622776602 x = 21.622776602 Simplifying x = 21.622776602Subproblem 2
x + 10 = -31.622776602 Simplifying x + 10 = -31.622776602 Reorder the terms: 10 + x = -31.622776602 Solving 10 + x = -31.622776602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -31.622776602 + -10 Combine like terms: 10 + -10 = 0 0 + x = -31.622776602 + -10 x = -31.622776602 + -10 Combine like terms: -31.622776602 + -10 = -41.622776602 x = -41.622776602 Simplifying x = -41.622776602Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.622776602, -41.622776602}
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