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Simplifying 96x2 + -105x + -224 = 0 Reorder the terms: -224 + -105x + 96x2 = 0 Solving -224 + -105x + 96x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 96 the coefficient of the squared term: Divide each side by '96'. -2.333333333 + -1.09375x + x2 = 0 Move the constant term to the right: Add '2.333333333' to each side of the equation. -2.333333333 + -1.09375x + 2.333333333 + x2 = 0 + 2.333333333 Reorder the terms: -2.333333333 + 2.333333333 + -1.09375x + x2 = 0 + 2.333333333 Combine like terms: -2.333333333 + 2.333333333 = 0.000000000 0.000000000 + -1.09375x + x2 = 0 + 2.333333333 -1.09375x + x2 = 0 + 2.333333333 Combine like terms: 0 + 2.333333333 = 2.333333333 -1.09375x + x2 = 2.333333333 The x term is -1.09375x. Take half its coefficient (-0.546875). Square it (0.2990722656) and add it to both sides. Add '0.2990722656' to each side of the equation. -1.09375x + 0.2990722656 + x2 = 2.333333333 + 0.2990722656 Reorder the terms: 0.2990722656 + -1.09375x + x2 = 2.333333333 + 0.2990722656 Combine like terms: 2.333333333 + 0.2990722656 = 2.6324055986 0.2990722656 + -1.09375x + x2 = 2.6324055986 Factor a perfect square on the left side: (x + -0.546875)(x + -0.546875) = 2.6324055986 Calculate the square root of the right side: 1.622468982 Break this problem into two subproblems by setting (x + -0.546875) equal to 1.622468982 and -1.622468982.Subproblem 1
x + -0.546875 = 1.622468982 Simplifying x + -0.546875 = 1.622468982 Reorder the terms: -0.546875 + x = 1.622468982 Solving -0.546875 + x = 1.622468982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.546875' to each side of the equation. -0.546875 + 0.546875 + x = 1.622468982 + 0.546875 Combine like terms: -0.546875 + 0.546875 = 0.000000 0.000000 + x = 1.622468982 + 0.546875 x = 1.622468982 + 0.546875 Combine like terms: 1.622468982 + 0.546875 = 2.169343982 x = 2.169343982 Simplifying x = 2.169343982Subproblem 2
x + -0.546875 = -1.622468982 Simplifying x + -0.546875 = -1.622468982 Reorder the terms: -0.546875 + x = -1.622468982 Solving -0.546875 + x = -1.622468982 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.546875' to each side of the equation. -0.546875 + 0.546875 + x = -1.622468982 + 0.546875 Combine like terms: -0.546875 + 0.546875 = 0.000000 0.000000 + x = -1.622468982 + 0.546875 x = -1.622468982 + 0.546875 Combine like terms: -1.622468982 + 0.546875 = -1.075593982 x = -1.075593982 Simplifying x = -1.075593982Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.169343982, -1.075593982}
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