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Simplifying 5x2 + -30x + 41 = 0 Reorder the terms: 41 + -30x + 5x2 = 0 Solving 41 + -30x + 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 + -6x + x2 = 0 Move the constant term to the right: Add '-8.2' to each side of the equation. 8.2 + -6x + -8.2 + x2 = 0 + -8.2 Reorder the terms: 8.2 + -8.2 + -6x + x2 = 0 + -8.2 Combine like terms: 8.2 + -8.2 = 0.0 0.0 + -6x + x2 = 0 + -8.2 -6x + x2 = 0 + -8.2 Combine like terms: 0 + -8.2 = -8.2 -6x + x2 = -8.2 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -8.2 + 9 Reorder the terms: 9 + -6x + x2 = -8.2 + 9 Combine like terms: -8.2 + 9 = 0.8 9 + -6x + x2 = 0.8 Factor a perfect square on the left side: (x + -3)(x + -3) = 0.8 Calculate the square root of the right side: 0.894427191 Break this problem into two subproblems by setting (x + -3) equal to 0.894427191 and -0.894427191.Subproblem 1
x + -3 = 0.894427191 Simplifying x + -3 = 0.894427191 Reorder the terms: -3 + x = 0.894427191 Solving -3 + x = 0.894427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 0.894427191 + 3 Combine like terms: -3 + 3 = 0 0 + x = 0.894427191 + 3 x = 0.894427191 + 3 Combine like terms: 0.894427191 + 3 = 3.894427191 x = 3.894427191 Simplifying x = 3.894427191Subproblem 2
x + -3 = -0.894427191 Simplifying x + -3 = -0.894427191 Reorder the terms: -3 + x = -0.894427191 Solving -3 + x = -0.894427191 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -0.894427191 + 3 Combine like terms: -3 + 3 = 0 0 + x = -0.894427191 + 3 x = -0.894427191 + 3 Combine like terms: -0.894427191 + 3 = 2.105572809 x = 2.105572809 Simplifying x = 2.105572809Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.894427191, 2.105572809}
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