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Simplifying 344.35 = 8x2 + -20x Reorder the terms: 344.35 = -20x + 8x2 Solving 344.35 = -20x + 8x2 Solving for variable 'x'. Reorder the terms: 344.35 + 20x + -8x2 = -20x + 20x + 8x2 + -8x2 Combine like terms: -20x + 20x = 0 344.35 + 20x + -8x2 = 0 + 8x2 + -8x2 344.35 + 20x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 344.35 + 20x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -43.04375 + -2.5x + x2 = 0 Move the constant term to the right: Add '43.04375' to each side of the equation. -43.04375 + -2.5x + 43.04375 + x2 = 0 + 43.04375 Reorder the terms: -43.04375 + 43.04375 + -2.5x + x2 = 0 + 43.04375 Combine like terms: -43.04375 + 43.04375 = 0.00000 0.00000 + -2.5x + x2 = 0 + 43.04375 -2.5x + x2 = 0 + 43.04375 Combine like terms: 0 + 43.04375 = 43.04375 -2.5x + x2 = 43.04375 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 43.04375 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 43.04375 + 1.5625 Combine like terms: 43.04375 + 1.5625 = 44.60625 1.5625 + -2.5x + x2 = 44.60625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 44.60625 Calculate the square root of the right side: 6.678791058 Break this problem into two subproblems by setting (x + -1.25) equal to 6.678791058 and -6.678791058.Subproblem 1
x + -1.25 = 6.678791058 Simplifying x + -1.25 = 6.678791058 Reorder the terms: -1.25 + x = 6.678791058 Solving -1.25 + x = 6.678791058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 6.678791058 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 6.678791058 + 1.25 x = 6.678791058 + 1.25 Combine like terms: 6.678791058 + 1.25 = 7.928791058 x = 7.928791058 Simplifying x = 7.928791058Subproblem 2
x + -1.25 = -6.678791058 Simplifying x + -1.25 = -6.678791058 Reorder the terms: -1.25 + x = -6.678791058 Solving -1.25 + x = -6.678791058 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -6.678791058 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -6.678791058 + 1.25 x = -6.678791058 + 1.25 Combine like terms: -6.678791058 + 1.25 = -5.428791058 x = -5.428791058 Simplifying x = -5.428791058Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.928791058, -5.428791058}
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