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Simplifying x2 + 20x + -19.8 = 0 Reorder the terms: -19.8 + 20x + x2 = 0 Solving -19.8 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '19.8' to each side of the equation. -19.8 + 20x + 19.8 + x2 = 0 + 19.8 Reorder the terms: -19.8 + 19.8 + 20x + x2 = 0 + 19.8 Combine like terms: -19.8 + 19.8 = 0.0 0.0 + 20x + x2 = 0 + 19.8 20x + x2 = 0 + 19.8 Combine like terms: 0 + 19.8 = 19.8 20x + x2 = 19.8 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 = 19.8 + 100 Reorder the terms: 100 + 20x + x2 = 19.8 + 100 Combine like terms: 19.8 + 100 = 119.8 100 + 20x + x2 = 119.8 Factor a perfect square on the left side: (x + 10)(x + 10) = 119.8 Calculate the square root of the right side: 10.945318634 Break this problem into two subproblems by setting (x + 10) equal to 10.945318634 and -10.945318634.Subproblem 1
x + 10 = 10.945318634 Simplifying x + 10 = 10.945318634 Reorder the terms: 10 + x = 10.945318634 Solving 10 + x = 10.945318634 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 = 10.945318634 + -10 Combine like terms: 10 + -10 = 0 0 + x = 10.945318634 + -10 x = 10.945318634 + -10 Combine like terms: 10.945318634 + -10 = 0.945318634 x = 0.945318634 Simplifying x = 0.945318634Subproblem 2
x + 10 = -10.945318634 Simplifying x + 10 = -10.945318634 Reorder the terms: 10 + x = -10.945318634 Solving 10 + x = -10.945318634 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 = -10.945318634 + -10 Combine like terms: 10 + -10 = 0 0 + x = -10.945318634 + -10 x = -10.945318634 + -10 Combine like terms: -10.945318634 + -10 = -20.945318634 x = -20.945318634 Simplifying x = -20.945318634Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.945318634, -20.945318634}
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