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Simplifying 0.01x2 + 0.2x + 0.6 = 0 Reorder the terms: 0.6 + 0.2x + 0.01x2 = 0 Solving 0.6 + 0.2x + 0.01x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.01 the coefficient of the squared term: Divide each side by '0.01'. 60 + 20x + x2 = 0 Move the constant term to the right: Add '-60' to each side of the equation. 60 + 20x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + 20x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + 20x + x2 = 0 + -60 20x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 20x + x2 = -60 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 = -60 + 100 Reorder the terms: 100 + 20x + x2 = -60 + 100 Combine like terms: -60 + 100 = 40 100 + 20x + x2 = 40 Factor a perfect square on the left side: (x + 10)(x + 10) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + 10) equal to 6.32455532 and -6.32455532.Subproblem 1
x + 10 = 6.32455532 Simplifying x + 10 = 6.32455532 Reorder the terms: 10 + x = 6.32455532 Solving 10 + x = 6.32455532 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 = 6.32455532 + -10 Combine like terms: 10 + -10 = 0 0 + x = 6.32455532 + -10 x = 6.32455532 + -10 Combine like terms: 6.32455532 + -10 = -3.67544468 x = -3.67544468 Simplifying x = -3.67544468Subproblem 2
x + 10 = -6.32455532 Simplifying x + 10 = -6.32455532 Reorder the terms: 10 + x = -6.32455532 Solving 10 + x = -6.32455532 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 = -6.32455532 + -10 Combine like terms: 10 + -10 = 0 0 + x = -6.32455532 + -10 x = -6.32455532 + -10 Combine like terms: -6.32455532 + -10 = -16.32455532 x = -16.32455532 Simplifying x = -16.32455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.67544468, -16.32455532}
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