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Simplifying 0.2x2 + 4.1x + -30 = 0 Reorder the terms: -30 + 4.1x + 0.2x2 = 0 Solving -30 + 4.1x + 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'. -150 + 20.5x + x2 = 0 Move the constant term to the right: Add '150' to each side of the equation. -150 + 20.5x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + 20.5x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + 20.5x + x2 = 0 + 150 20.5x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 20.5x + x2 = 150 The x term is 20.5x. Take half its coefficient (10.25). Square it (105.0625) and add it to both sides. Add '105.0625' to each side of the equation. 20.5x + 105.0625 + x2 = 150 + 105.0625 Reorder the terms: 105.0625 + 20.5x + x2 = 150 + 105.0625 Combine like terms: 150 + 105.0625 = 255.0625 105.0625 + 20.5x + x2 = 255.0625 Factor a perfect square on the left side: (x + 10.25)(x + 10.25) = 255.0625 Calculate the square root of the right side: 15.970676254 Break this problem into two subproblems by setting (x + 10.25) equal to 15.970676254 and -15.970676254.Subproblem 1
x + 10.25 = 15.970676254 Simplifying x + 10.25 = 15.970676254 Reorder the terms: 10.25 + x = 15.970676254 Solving 10.25 + x = 15.970676254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.25' to each side of the equation. 10.25 + -10.25 + x = 15.970676254 + -10.25 Combine like terms: 10.25 + -10.25 = 0.00 0.00 + x = 15.970676254 + -10.25 x = 15.970676254 + -10.25 Combine like terms: 15.970676254 + -10.25 = 5.720676254 x = 5.720676254 Simplifying x = 5.720676254Subproblem 2
x + 10.25 = -15.970676254 Simplifying x + 10.25 = -15.970676254 Reorder the terms: 10.25 + x = -15.970676254 Solving 10.25 + x = -15.970676254 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.25' to each side of the equation. 10.25 + -10.25 + x = -15.970676254 + -10.25 Combine like terms: 10.25 + -10.25 = 0.00 0.00 + x = -15.970676254 + -10.25 x = -15.970676254 + -10.25 Combine like terms: -15.970676254 + -10.25 = -26.220676254 x = -26.220676254 Simplifying x = -26.220676254Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.720676254, -26.220676254}
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