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Simplifying 2x2 + 41x + -224 = 0 Reorder the terms: -224 + 41x + 2x2 = 0 Solving -224 + 41x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -112 + 20.5x + x2 = 0 Move the constant term to the right: Add '112' to each side of the equation. -112 + 20.5x + 112 + x2 = 0 + 112 Reorder the terms: -112 + 112 + 20.5x + x2 = 0 + 112 Combine like terms: -112 + 112 = 0 0 + 20.5x + x2 = 0 + 112 20.5x + x2 = 0 + 112 Combine like terms: 0 + 112 = 112 20.5x + x2 = 112 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 = 112 + 105.0625 Reorder the terms: 105.0625 + 20.5x + x2 = 112 + 105.0625 Combine like terms: 112 + 105.0625 = 217.0625 105.0625 + 20.5x + x2 = 217.0625 Factor a perfect square on the left side: (x + 10.25)(x + 10.25) = 217.0625 Calculate the square root of the right side: 14.733041098 Break this problem into two subproblems by setting (x + 10.25) equal to 14.733041098 and -14.733041098.Subproblem 1
x + 10.25 = 14.733041098 Simplifying x + 10.25 = 14.733041098 Reorder the terms: 10.25 + x = 14.733041098 Solving 10.25 + x = 14.733041098 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 = 14.733041098 + -10.25 Combine like terms: 10.25 + -10.25 = 0.00 0.00 + x = 14.733041098 + -10.25 x = 14.733041098 + -10.25 Combine like terms: 14.733041098 + -10.25 = 4.483041098 x = 4.483041098 Simplifying x = 4.483041098Subproblem 2
x + 10.25 = -14.733041098 Simplifying x + 10.25 = -14.733041098 Reorder the terms: 10.25 + x = -14.733041098 Solving 10.25 + x = -14.733041098 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 = -14.733041098 + -10.25 Combine like terms: 10.25 + -10.25 = 0.00 0.00 + x = -14.733041098 + -10.25 x = -14.733041098 + -10.25 Combine like terms: -14.733041098 + -10.25 = -24.983041098 x = -24.983041098 Simplifying x = -24.983041098Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.483041098, -24.983041098}
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