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Simplifying x2 + -10.4625x + 27.04 = 0 Reorder the terms: 27.04 + -10.4625x + x2 = 0 Solving 27.04 + -10.4625x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-27.04' to each side of the equation. 27.04 + -10.4625x + -27.04 + x2 = 0 + -27.04 Reorder the terms: 27.04 + -27.04 + -10.4625x + x2 = 0 + -27.04 Combine like terms: 27.04 + -27.04 = 0.00 0.00 + -10.4625x + x2 = 0 + -27.04 -10.4625x + x2 = 0 + -27.04 Combine like terms: 0 + -27.04 = -27.04 -10.4625x + x2 = -27.04 The x term is -10.4625x. Take half its coefficient (-5.23125). Square it (27.36597656) and add it to both sides. Add '27.36597656' to each side of the equation. -10.4625x + 27.36597656 + x2 = -27.04 + 27.36597656 Reorder the terms: 27.36597656 + -10.4625x + x2 = -27.04 + 27.36597656 Combine like terms: -27.04 + 27.36597656 = 0.32597656 27.36597656 + -10.4625x + x2 = 0.32597656 Factor a perfect square on the left side: (x + -5.23125)(x + -5.23125) = 0.32597656 Calculate the square root of the right side: 0.57094357 Break this problem into two subproblems by setting (x + -5.23125) equal to 0.57094357 and -0.57094357.Subproblem 1
x + -5.23125 = 0.57094357 Simplifying x + -5.23125 = 0.57094357 Reorder the terms: -5.23125 + x = 0.57094357 Solving -5.23125 + x = 0.57094357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.23125' to each side of the equation. -5.23125 + 5.23125 + x = 0.57094357 + 5.23125 Combine like terms: -5.23125 + 5.23125 = 0.00000 0.00000 + x = 0.57094357 + 5.23125 x = 0.57094357 + 5.23125 Combine like terms: 0.57094357 + 5.23125 = 5.80219357 x = 5.80219357 Simplifying x = 5.80219357Subproblem 2
x + -5.23125 = -0.57094357 Simplifying x + -5.23125 = -0.57094357 Reorder the terms: -5.23125 + x = -0.57094357 Solving -5.23125 + x = -0.57094357 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.23125' to each side of the equation. -5.23125 + 5.23125 + x = -0.57094357 + 5.23125 Combine like terms: -5.23125 + 5.23125 = 0.00000 0.00000 + x = -0.57094357 + 5.23125 x = -0.57094357 + 5.23125 Combine like terms: -0.57094357 + 5.23125 = 4.66030643 x = 4.66030643 Simplifying x = 4.66030643Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.80219357, 4.66030643}
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