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Simplifying 0 = 5x2 + 41x + -8 Reorder the terms: 0 = -8 + 41x + 5x2 Solving 0 = -8 + 41x + 5x2 Solving for variable 'x'. Combine like terms: 0 + 8 = 8 8 + -41x + -5x2 = -8 + 41x + 5x2 + 8 + -41x + -5x2 Reorder the terms: 8 + -41x + -5x2 = -8 + 8 + 41x + -41x + 5x2 + -5x2 Combine like terms: -8 + 8 = 0 8 + -41x + -5x2 = 0 + 41x + -41x + 5x2 + -5x2 8 + -41x + -5x2 = 41x + -41x + 5x2 + -5x2 Combine like terms: 41x + -41x = 0 8 + -41x + -5x2 = 0 + 5x2 + -5x2 8 + -41x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 8 + -41x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -1.6 + 8.2x + x2 = 0 Move the constant term to the right: Add '1.6' to each side of the equation. -1.6 + 8.2x + 1.6 + x2 = 0 + 1.6 Reorder the terms: -1.6 + 1.6 + 8.2x + x2 = 0 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + 8.2x + x2 = 0 + 1.6 8.2x + x2 = 0 + 1.6 Combine like terms: 0 + 1.6 = 1.6 8.2x + x2 = 1.6 The x term is 8.2x. Take half its coefficient (4.1). Square it (16.81) and add it to both sides. Add '16.81' to each side of the equation. 8.2x + 16.81 + x2 = 1.6 + 16.81 Reorder the terms: 16.81 + 8.2x + x2 = 1.6 + 16.81 Combine like terms: 1.6 + 16.81 = 18.41 16.81 + 8.2x + x2 = 18.41 Factor a perfect square on the left side: (x + 4.1)(x + 4.1) = 18.41 Calculate the square root of the right side: 4.290687591 Break this problem into two subproblems by setting (x + 4.1) equal to 4.290687591 and -4.290687591.Subproblem 1
x + 4.1 = 4.290687591 Simplifying x + 4.1 = 4.290687591 Reorder the terms: 4.1 + x = 4.290687591 Solving 4.1 + x = 4.290687591 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.1' to each side of the equation. 4.1 + -4.1 + x = 4.290687591 + -4.1 Combine like terms: 4.1 + -4.1 = 0.0 0.0 + x = 4.290687591 + -4.1 x = 4.290687591 + -4.1 Combine like terms: 4.290687591 + -4.1 = 0.190687591 x = 0.190687591 Simplifying x = 0.190687591Subproblem 2
x + 4.1 = -4.290687591 Simplifying x + 4.1 = -4.290687591 Reorder the terms: 4.1 + x = -4.290687591 Solving 4.1 + x = -4.290687591 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.1' to each side of the equation. 4.1 + -4.1 + x = -4.290687591 + -4.1 Combine like terms: 4.1 + -4.1 = 0.0 0.0 + x = -4.290687591 + -4.1 x = -4.290687591 + -4.1 Combine like terms: -4.290687591 + -4.1 = -8.390687591 x = -8.390687591 Simplifying x = -8.390687591Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.190687591, -8.390687591}
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