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Simplifying 2x2 + 43x + -2730 = 0 Reorder the terms: -2730 + 43x + 2x2 = 0 Solving -2730 + 43x + 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'. -1365 + 21.5x + x2 = 0 Move the constant term to the right: Add '1365' to each side of the equation. -1365 + 21.5x + 1365 + x2 = 0 + 1365 Reorder the terms: -1365 + 1365 + 21.5x + x2 = 0 + 1365 Combine like terms: -1365 + 1365 = 0 0 + 21.5x + x2 = 0 + 1365 21.5x + x2 = 0 + 1365 Combine like terms: 0 + 1365 = 1365 21.5x + x2 = 1365 The x term is 21.5x. Take half its coefficient (10.75). Square it (115.5625) and add it to both sides. Add '115.5625' to each side of the equation. 21.5x + 115.5625 + x2 = 1365 + 115.5625 Reorder the terms: 115.5625 + 21.5x + x2 = 1365 + 115.5625 Combine like terms: 1365 + 115.5625 = 1480.5625 115.5625 + 21.5x + x2 = 1480.5625 Factor a perfect square on the left side: (x + 10.75)(x + 10.75) = 1480.5625 Calculate the square root of the right side: 38.478078174 Break this problem into two subproblems by setting (x + 10.75) equal to 38.478078174 and -38.478078174.Subproblem 1
x + 10.75 = 38.478078174 Simplifying x + 10.75 = 38.478078174 Reorder the terms: 10.75 + x = 38.478078174 Solving 10.75 + x = 38.478078174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.75' to each side of the equation. 10.75 + -10.75 + x = 38.478078174 + -10.75 Combine like terms: 10.75 + -10.75 = 0.00 0.00 + x = 38.478078174 + -10.75 x = 38.478078174 + -10.75 Combine like terms: 38.478078174 + -10.75 = 27.728078174 x = 27.728078174 Simplifying x = 27.728078174Subproblem 2
x + 10.75 = -38.478078174 Simplifying x + 10.75 = -38.478078174 Reorder the terms: 10.75 + x = -38.478078174 Solving 10.75 + x = -38.478078174 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.75' to each side of the equation. 10.75 + -10.75 + x = -38.478078174 + -10.75 Combine like terms: 10.75 + -10.75 = 0.00 0.00 + x = -38.478078174 + -10.75 x = -38.478078174 + -10.75 Combine like terms: -38.478078174 + -10.75 = -49.228078174 x = -49.228078174 Simplifying x = -49.228078174Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.728078174, -49.228078174}
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