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Simplifying 0.2x2 + 20x + 81 = 0 Reorder the terms: 81 + 20x + 0.2x2 = 0 Solving 81 + 20x + 0.2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 405 + 100x + x2 = 0 Move the constant term to the right: Add '-405' to each side of the equation. 405 + 100x + -405 + x2 = 0 + -405 Reorder the terms: 405 + -405 + 100x + x2 = 0 + -405 Combine like terms: 405 + -405 = 0 0 + 100x + x2 = 0 + -405 100x + x2 = 0 + -405 Combine like terms: 0 + -405 = -405 100x + x2 = -405 The x term is 100x. Take half its coefficient (50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. 100x + 2500 + x2 = -405 + 2500 Reorder the terms: 2500 + 100x + x2 = -405 + 2500 Combine like terms: -405 + 2500 = 2095 2500 + 100x + x2 = 2095 Factor a perfect square on the left side: (x + 50)(x + 50) = 2095 Calculate the square root of the right side: 45.771169965 Break this problem into two subproblems by setting (x + 50) equal to 45.771169965 and -45.771169965.Subproblem 1
x + 50 = 45.771169965 Simplifying x + 50 = 45.771169965 Reorder the terms: 50 + x = 45.771169965 Solving 50 + x = 45.771169965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = 45.771169965 + -50 Combine like terms: 50 + -50 = 0 0 + x = 45.771169965 + -50 x = 45.771169965 + -50 Combine like terms: 45.771169965 + -50 = -4.228830035 x = -4.228830035 Simplifying x = -4.228830035Subproblem 2
x + 50 = -45.771169965 Simplifying x + 50 = -45.771169965 Reorder the terms: 50 + x = -45.771169965 Solving 50 + x = -45.771169965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + x = -45.771169965 + -50 Combine like terms: 50 + -50 = 0 0 + x = -45.771169965 + -50 x = -45.771169965 + -50 Combine like terms: -45.771169965 + -50 = -95.771169965 x = -95.771169965 Simplifying x = -95.771169965Solution
The solution to the problem is based on the solutions from the subproblems. x = {-4.228830035, -95.771169965}
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