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Simplifying 5x2 + -41x + 46 = 0 Reorder the terms: 46 + -41x + 5x2 = 0 Solving 46 + -41x + 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'. 9.2 + -8.2x + x2 = 0 Move the constant term to the right: Add '-9.2' to each side of the equation. 9.2 + -8.2x + -9.2 + x2 = 0 + -9.2 Reorder the terms: 9.2 + -9.2 + -8.2x + x2 = 0 + -9.2 Combine like terms: 9.2 + -9.2 = 0.0 0.0 + -8.2x + x2 = 0 + -9.2 -8.2x + x2 = 0 + -9.2 Combine like terms: 0 + -9.2 = -9.2 -8.2x + x2 = -9.2 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 = -9.2 + 16.81 Reorder the terms: 16.81 + -8.2x + x2 = -9.2 + 16.81 Combine like terms: -9.2 + 16.81 = 7.61 16.81 + -8.2x + x2 = 7.61 Factor a perfect square on the left side: (x + -4.1)(x + -4.1) = 7.61 Calculate the square root of the right side: 2.758622845 Break this problem into two subproblems by setting (x + -4.1) equal to 2.758622845 and -2.758622845.Subproblem 1
x + -4.1 = 2.758622845 Simplifying x + -4.1 = 2.758622845 Reorder the terms: -4.1 + x = 2.758622845 Solving -4.1 + x = 2.758622845 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 = 2.758622845 + 4.1 Combine like terms: -4.1 + 4.1 = 0.0 0.0 + x = 2.758622845 + 4.1 x = 2.758622845 + 4.1 Combine like terms: 2.758622845 + 4.1 = 6.858622845 x = 6.858622845 Simplifying x = 6.858622845Subproblem 2
x + -4.1 = -2.758622845 Simplifying x + -4.1 = -2.758622845 Reorder the terms: -4.1 + x = -2.758622845 Solving -4.1 + x = -2.758622845 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 = -2.758622845 + 4.1 Combine like terms: -4.1 + 4.1 = 0.0 0.0 + x = -2.758622845 + 4.1 x = -2.758622845 + 4.1 Combine like terms: -2.758622845 + 4.1 = 1.341377155 x = 1.341377155 Simplifying x = 1.341377155Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.858622845, 1.341377155}
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