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Simplifying 24x2 + -75x + -29 = 0 Reorder the terms: -29 + -75x + 24x2 = 0 Solving -29 + -75x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -1.208333333 + -3.125x + x2 = 0 Move the constant term to the right: Add '1.208333333' to each side of the equation. -1.208333333 + -3.125x + 1.208333333 + x2 = 0 + 1.208333333 Reorder the terms: -1.208333333 + 1.208333333 + -3.125x + x2 = 0 + 1.208333333 Combine like terms: -1.208333333 + 1.208333333 = 0.000000000 0.000000000 + -3.125x + x2 = 0 + 1.208333333 -3.125x + x2 = 0 + 1.208333333 Combine like terms: 0 + 1.208333333 = 1.208333333 -3.125x + x2 = 1.208333333 The x term is -3.125x. Take half its coefficient (-1.5625). Square it (2.44140625) and add it to both sides. Add '2.44140625' to each side of the equation. -3.125x + 2.44140625 + x2 = 1.208333333 + 2.44140625 Reorder the terms: 2.44140625 + -3.125x + x2 = 1.208333333 + 2.44140625 Combine like terms: 1.208333333 + 2.44140625 = 3.649739583 2.44140625 + -3.125x + x2 = 3.649739583 Factor a perfect square on the left side: (x + -1.5625)(x + -1.5625) = 3.649739583 Calculate the square root of the right side: 1.910429162 Break this problem into two subproblems by setting (x + -1.5625) equal to 1.910429162 and -1.910429162.Subproblem 1
x + -1.5625 = 1.910429162 Simplifying x + -1.5625 = 1.910429162 Reorder the terms: -1.5625 + x = 1.910429162 Solving -1.5625 + x = 1.910429162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = 1.910429162 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = 1.910429162 + 1.5625 x = 1.910429162 + 1.5625 Combine like terms: 1.910429162 + 1.5625 = 3.472929162 x = 3.472929162 Simplifying x = 3.472929162Subproblem 2
x + -1.5625 = -1.910429162 Simplifying x + -1.5625 = -1.910429162 Reorder the terms: -1.5625 + x = -1.910429162 Solving -1.5625 + x = -1.910429162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5625' to each side of the equation. -1.5625 + 1.5625 + x = -1.910429162 + 1.5625 Combine like terms: -1.5625 + 1.5625 = 0.0000 0.0000 + x = -1.910429162 + 1.5625 x = -1.910429162 + 1.5625 Combine like terms: -1.910429162 + 1.5625 = -0.347929162 x = -0.347929162 Simplifying x = -0.347929162Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.472929162, -0.347929162}
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