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Simplifying 5.76X2 + 2.86X + -1.35 = 8 Reorder the terms: -1.35 + 2.86X + 5.76X2 = 8 Solving -1.35 + 2.86X + 5.76X2 = 8 Solving for variable 'X'. Reorder the terms: -1.35 + -8 + 2.86X + 5.76X2 = 8 + -8 Combine like terms: -1.35 + -8 = -9.35 -9.35 + 2.86X + 5.76X2 = 8 + -8 Combine like terms: 8 + -8 = 0 -9.35 + 2.86X + 5.76X2 = 0 Begin completing the square. Divide all terms by 5.76 the coefficient of the squared term: Divide each side by '5.76'. -1.623263889 + 0.4965277778X + X2 = 0 Move the constant term to the right: Add '1.623263889' to each side of the equation. -1.623263889 + 0.4965277778X + 1.623263889 + X2 = 0 + 1.623263889 Reorder the terms: -1.623263889 + 1.623263889 + 0.4965277778X + X2 = 0 + 1.623263889 Combine like terms: -1.623263889 + 1.623263889 = 0.000000000 0.000000000 + 0.4965277778X + X2 = 0 + 1.623263889 0.4965277778X + X2 = 0 + 1.623263889 Combine like terms: 0 + 1.623263889 = 1.623263889 0.4965277778X + X2 = 1.623263889 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 = 1.623263889 + 0.06163495853 Reorder the terms: 0.06163495853 + 0.4965277778X + X2 = 1.623263889 + 0.06163495853 Combine like terms: 1.623263889 + 0.06163495853 = 1.68489884753 0.06163495853 + 0.4965277778X + X2 = 1.68489884753 Factor a perfect square on the left side: (X + 0.2482638889)(X + 0.2482638889) = 1.68489884753 Calculate the square root of the right side: 1.298036536 Break this problem into two subproblems by setting (X + 0.2482638889) equal to 1.298036536 and -1.298036536.Subproblem 1
X + 0.2482638889 = 1.298036536 Simplifying X + 0.2482638889 = 1.298036536 Reorder the terms: 0.2482638889 + X = 1.298036536 Solving 0.2482638889 + X = 1.298036536 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 = 1.298036536 + -0.2482638889 Combine like terms: 0.2482638889 + -0.2482638889 = 0.0000000000 0.0000000000 + X = 1.298036536 + -0.2482638889 X = 1.298036536 + -0.2482638889 Combine like terms: 1.298036536 + -0.2482638889 = 1.0497726471 X = 1.0497726471 Simplifying X = 1.0497726471Subproblem 2
X + 0.2482638889 = -1.298036536 Simplifying X + 0.2482638889 = -1.298036536 Reorder the terms: 0.2482638889 + X = -1.298036536 Solving 0.2482638889 + X = -1.298036536 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 = -1.298036536 + -0.2482638889 Combine like terms: 0.2482638889 + -0.2482638889 = 0.0000000000 0.0000000000 + X = -1.298036536 + -0.2482638889 X = -1.298036536 + -0.2482638889 Combine like terms: -1.298036536 + -0.2482638889 = -1.5463004249 X = -1.5463004249 Simplifying X = -1.5463004249Solution
The solution to the problem is based on the solutions from the subproblems. X = {1.0497726471, -1.5463004249}
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