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Simplifying 60 = 0.05x2 + x Reorder the terms: 60 = x + 0.05x2 Solving 60 = x + 0.05x2 Solving for variable 'x'. Reorder the terms: 60 + -1x + -0.05x2 = x + -1x + 0.05x2 + -0.05x2 Combine like terms: x + -1x = 0 60 + -1x + -0.05x2 = 0 + 0.05x2 + -0.05x2 60 + -1x + -0.05x2 = 0.05x2 + -0.05x2 Combine like terms: 0.05x2 + -0.05x2 = 0.00 60 + -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'. -1200 + 20x + x2 = 0 Move the constant term to the right: Add '1200' to each side of the equation. -1200 + 20x + 1200 + x2 = 0 + 1200 Reorder the terms: -1200 + 1200 + 20x + x2 = 0 + 1200 Combine like terms: -1200 + 1200 = 0 0 + 20x + x2 = 0 + 1200 20x + x2 = 0 + 1200 Combine like terms: 0 + 1200 = 1200 20x + x2 = 1200 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 = 1200 + 100 Reorder the terms: 100 + 20x + x2 = 1200 + 100 Combine like terms: 1200 + 100 = 1300 100 + 20x + x2 = 1300 Factor a perfect square on the left side: (x + 10)(x + 10) = 1300 Calculate the square root of the right side: 36.055512755 Break this problem into two subproblems by setting (x + 10) equal to 36.055512755 and -36.055512755.Subproblem 1
x + 10 = 36.055512755 Simplifying x + 10 = 36.055512755 Reorder the terms: 10 + x = 36.055512755 Solving 10 + x = 36.055512755 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 = 36.055512755 + -10 Combine like terms: 10 + -10 = 0 0 + x = 36.055512755 + -10 x = 36.055512755 + -10 Combine like terms: 36.055512755 + -10 = 26.055512755 x = 26.055512755 Simplifying x = 26.055512755Subproblem 2
x + 10 = -36.055512755 Simplifying x + 10 = -36.055512755 Reorder the terms: 10 + x = -36.055512755 Solving 10 + x = -36.055512755 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 = -36.055512755 + -10 Combine like terms: 10 + -10 = 0 0 + x = -36.055512755 + -10 x = -36.055512755 + -10 Combine like terms: -36.055512755 + -10 = -46.055512755 x = -46.055512755 Simplifying x = -46.055512755Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.055512755, -46.055512755}
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