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Simplifying (1.6x * 1.6x) + 24x + 45 = 0 Reorder the terms for easier multiplication: (1.6 * 1.6x * x) + 24x + 45 = 0 Multiply 1.6 * 1.6 (2.56x * x) + 24x + 45 = 0 Multiply x * x (2.56x2) + 24x + 45 = 0 Reorder the terms: 45 + 24x + (2.56x2) = 0 Solving 45 + 24x + (2.56x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.56 the coefficient of the squared term: Divide each side by '2.56'. 17.578125 + 9.375x + x2 = 0 Move the constant term to the right: Add '-17.578125' to each side of the equation. 17.578125 + 9.375x + -17.578125 + x2 = 0 + -17.578125 Reorder the terms: 17.578125 + -17.578125 + 9.375x + x2 = 0 + -17.578125 Combine like terms: 17.578125 + -17.578125 = 0.000000 0.000000 + 9.375x + x2 = 0 + -17.578125 9.375x + x2 = 0 + -17.578125 Combine like terms: 0 + -17.578125 = -17.578125 9.375x + x2 = -17.578125 The x term is 9.375x. Take half its coefficient (4.6875). Square it (21.97265625) and add it to both sides. Add '21.97265625' to each side of the equation. 9.375x + 21.97265625 + x2 = -17.578125 + 21.97265625 Reorder the terms: 21.97265625 + 9.375x + x2 = -17.578125 + 21.97265625 Combine like terms: -17.578125 + 21.97265625 = 4.39453125 21.97265625 + 9.375x + x2 = 4.39453125 Factor a perfect square on the left side: ((x) + 4.6875)((x) + 4.6875) = 4.39453125 Calculate the square root of the right side: 2.096313729 Break this problem into two subproblems by setting ((x) + 4.6875) equal to 2.096313729 and -2.096313729.Subproblem 1
(x) + 4.6875 = 2.096313729 Simplifying (x) + 4.6875 = 2.096313729 x + 4.6875 = 2.096313729 Reorder the terms: 4.6875 + x = 2.096313729 Solving 4.6875 + x = 2.096313729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.6875' to each side of the equation. 4.6875 + -4.6875 + x = 2.096313729 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + x = 2.096313729 + -4.6875 x = 2.096313729 + -4.6875 Combine like terms: 2.096313729 + -4.6875 = -2.591186271 x = -2.591186271 Simplifying x = -2.591186271Subproblem 2
(x) + 4.6875 = -2.096313729 Simplifying (x) + 4.6875 = -2.096313729 x + 4.6875 = -2.096313729 Reorder the terms: 4.6875 + x = -2.096313729 Solving 4.6875 + x = -2.096313729 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.6875' to each side of the equation. 4.6875 + -4.6875 + x = -2.096313729 + -4.6875 Combine like terms: 4.6875 + -4.6875 = 0.0000 0.0000 + x = -2.096313729 + -4.6875 x = -2.096313729 + -4.6875 Combine like terms: -2.096313729 + -4.6875 = -6.783813729 x = -6.783813729 Simplifying x = -6.783813729Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.591186271, -6.783813729}
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