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Simplifying 5x2 + 19x + -41 = 0 Reorder the terms: -41 + 19x + 5x2 = 0 Solving -41 + 19x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -8.2 + 3.8x + x2 = 0 Move the constant term to the right: Add '8.2' to each side of the equation. -8.2 + 3.8x + 8.2 + x2 = 0 + 8.2 Reorder the terms: -8.2 + 8.2 + 3.8x + x2 = 0 + 8.2 Combine like terms: -8.2 + 8.2 = 0.0 0.0 + 3.8x + x2 = 0 + 8.2 3.8x + x2 = 0 + 8.2 Combine like terms: 0 + 8.2 = 8.2 3.8x + x2 = 8.2 The x term is 3.8x. Take half its coefficient (1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. 3.8x + 3.61 + x2 = 8.2 + 3.61 Reorder the terms: 3.61 + 3.8x + x2 = 8.2 + 3.61 Combine like terms: 8.2 + 3.61 = 11.81 3.61 + 3.8x + x2 = 11.81 Factor a perfect square on the left side: (x + 1.9)(x + 1.9) = 11.81 Calculate the square root of the right side: 3.436568055 Break this problem into two subproblems by setting (x + 1.9) equal to 3.436568055 and -3.436568055.Subproblem 1
x + 1.9 = 3.436568055 Simplifying x + 1.9 = 3.436568055 Reorder the terms: 1.9 + x = 3.436568055 Solving 1.9 + x = 3.436568055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = 3.436568055 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = 3.436568055 + -1.9 x = 3.436568055 + -1.9 Combine like terms: 3.436568055 + -1.9 = 1.536568055 x = 1.536568055 Simplifying x = 1.536568055Subproblem 2
x + 1.9 = -3.436568055 Simplifying x + 1.9 = -3.436568055 Reorder the terms: 1.9 + x = -3.436568055 Solving 1.9 + x = -3.436568055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = -3.436568055 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = -3.436568055 + -1.9 x = -3.436568055 + -1.9 Combine like terms: -3.436568055 + -1.9 = -5.336568055 x = -5.336568055 Simplifying x = -5.336568055Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.536568055, -5.336568055}
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