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Simplifying 5.76x2 + 2.86x + -1.35 = 0 Reorder the terms: -1.35 + 2.86x + 5.76x2 = 0 Solving -1.35 + 2.86x + 5.76x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5.76 the coefficient of the squared term: Divide each side by '5.76'. -0.234375 + 0.4965277778x + x2 = 0 Move the constant term to the right: Add '0.234375' to each side of the equation. -0.234375 + 0.4965277778x + 0.234375 + x2 = 0 + 0.234375 Reorder the terms: -0.234375 + 0.234375 + 0.4965277778x + x2 = 0 + 0.234375 Combine like terms: -0.234375 + 0.234375 = 0.000000 0.000000 + 0.4965277778x + x2 = 0 + 0.234375 0.4965277778x + x2 = 0 + 0.234375 Combine like terms: 0 + 0.234375 = 0.234375 0.4965277778x + x2 = 0.234375 The x term is 0.4965277778x. Take half its coefficient (0.2482638889). Square it (0.06163495853) and add it to both sides. Add '0.06163495853' to each side of the equation. 0.4965277778x + 0.06163495853 + x2 = 0.234375 + 0.06163495853 Reorder the terms: 0.06163495853 + 0.4965277778x + x2 = 0.234375 + 0.06163495853 Combine like terms: 0.234375 + 0.06163495853 = 0.29600995853 0.06163495853 + 0.4965277778x + x2 = 0.29600995853 Factor a perfect square on the left side: (x + 0.2482638889)(x + 0.2482638889) = 0.29600995853 Calculate the square root of the right side: 0.544067972 Break this problem into two subproblems by setting (x + 0.2482638889) equal to 0.544067972 and -0.544067972.Subproblem 1
x + 0.2482638889 = 0.544067972 Simplifying x + 0.2482638889 = 0.544067972 Reorder the terms: 0.2482638889 + x = 0.544067972 Solving 0.2482638889 + x = 0.544067972 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2482638889' to each side of the equation. 0.2482638889 + -0.2482638889 + x = 0.544067972 + -0.2482638889 Combine like terms: 0.2482638889 + -0.2482638889 = 0.0000000000 0.0000000000 + x = 0.544067972 + -0.2482638889 x = 0.544067972 + -0.2482638889 Combine like terms: 0.544067972 + -0.2482638889 = 0.2958040831 x = 0.2958040831 Simplifying x = 0.2958040831Subproblem 2
x + 0.2482638889 = -0.544067972 Simplifying x + 0.2482638889 = -0.544067972 Reorder the terms: 0.2482638889 + x = -0.544067972 Solving 0.2482638889 + x = -0.544067972 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2482638889' to each side of the equation. 0.2482638889 + -0.2482638889 + x = -0.544067972 + -0.2482638889 Combine like terms: 0.2482638889 + -0.2482638889 = 0.0000000000 0.0000000000 + x = -0.544067972 + -0.2482638889 x = -0.544067972 + -0.2482638889 Combine like terms: -0.544067972 + -0.2482638889 = -0.7923318609 x = -0.7923318609 Simplifying x = -0.7923318609Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.2958040831, -0.7923318609}
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