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Simplifying 4x2 + -75x + 24 = 0 Reorder the terms: 24 + -75x + 4x2 = 0 Solving 24 + -75x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 6 + -18.75x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -18.75x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -18.75x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -18.75x + x2 = 0 + -6 -18.75x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -18.75x + x2 = -6 The x term is -18.75x. Take half its coefficient (-9.375). Square it (87.890625) and add it to both sides. Add '87.890625' to each side of the equation. -18.75x + 87.890625 + x2 = -6 + 87.890625 Reorder the terms: 87.890625 + -18.75x + x2 = -6 + 87.890625 Combine like terms: -6 + 87.890625 = 81.890625 87.890625 + -18.75x + x2 = 81.890625 Factor a perfect square on the left side: (x + -9.375)(x + -9.375) = 81.890625 Calculate the square root of the right side: 9.049343899 Break this problem into two subproblems by setting (x + -9.375) equal to 9.049343899 and -9.049343899.Subproblem 1
x + -9.375 = 9.049343899 Simplifying x + -9.375 = 9.049343899 Reorder the terms: -9.375 + x = 9.049343899 Solving -9.375 + x = 9.049343899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.375' to each side of the equation. -9.375 + 9.375 + x = 9.049343899 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + x = 9.049343899 + 9.375 x = 9.049343899 + 9.375 Combine like terms: 9.049343899 + 9.375 = 18.424343899 x = 18.424343899 Simplifying x = 18.424343899Subproblem 2
x + -9.375 = -9.049343899 Simplifying x + -9.375 = -9.049343899 Reorder the terms: -9.375 + x = -9.049343899 Solving -9.375 + x = -9.049343899 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.375' to each side of the equation. -9.375 + 9.375 + x = -9.049343899 + 9.375 Combine like terms: -9.375 + 9.375 = 0.000 0.000 + x = -9.049343899 + 9.375 x = -9.049343899 + 9.375 Combine like terms: -9.049343899 + 9.375 = 0.325656101 x = 0.325656101 Simplifying x = 0.325656101Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.424343899, 0.325656101}
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