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Simplifying 20x2 + 38x + 5 = 0 Reorder the terms: 5 + 38x + 20x2 = 0 Solving 5 + 38x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.25 + 1.9x + x2 = 0 Move the constant term to the right: Add '-0.25' to each side of the equation. 0.25 + 1.9x + -0.25 + x2 = 0 + -0.25 Reorder the terms: 0.25 + -0.25 + 1.9x + x2 = 0 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + 1.9x + x2 = 0 + -0.25 1.9x + x2 = 0 + -0.25 Combine like terms: 0 + -0.25 = -0.25 1.9x + x2 = -0.25 The x term is 1.9x. Take half its coefficient (0.95). Square it (0.9025) and add it to both sides. Add '0.9025' to each side of the equation. 1.9x + 0.9025 + x2 = -0.25 + 0.9025 Reorder the terms: 0.9025 + 1.9x + x2 = -0.25 + 0.9025 Combine like terms: -0.25 + 0.9025 = 0.6525 0.9025 + 1.9x + x2 = 0.6525 Factor a perfect square on the left side: (x + 0.95)(x + 0.95) = 0.6525 Calculate the square root of the right side: 0.807774721 Break this problem into two subproblems by setting (x + 0.95) equal to 0.807774721 and -0.807774721.Subproblem 1
x + 0.95 = 0.807774721 Simplifying x + 0.95 = 0.807774721 Reorder the terms: 0.95 + x = 0.807774721 Solving 0.95 + x = 0.807774721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.95' to each side of the equation. 0.95 + -0.95 + x = 0.807774721 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 0.00 + x = 0.807774721 + -0.95 x = 0.807774721 + -0.95 Combine like terms: 0.807774721 + -0.95 = -0.142225279 x = -0.142225279 Simplifying x = -0.142225279Subproblem 2
x + 0.95 = -0.807774721 Simplifying x + 0.95 = -0.807774721 Reorder the terms: 0.95 + x = -0.807774721 Solving 0.95 + x = -0.807774721 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.95' to each side of the equation. 0.95 + -0.95 + x = -0.807774721 + -0.95 Combine like terms: 0.95 + -0.95 = 0.00 0.00 + x = -0.807774721 + -0.95 x = -0.807774721 + -0.95 Combine like terms: -0.807774721 + -0.95 = -1.757774721 x = -1.757774721 Simplifying x = -1.757774721Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.142225279, -1.757774721}
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