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Simplifying 24x2 + -41x + -58 = 0 Reorder the terms: -58 + -41x + 24x2 = 0 Solving -58 + -41x + 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'. -2.416666667 + -1.708333333x + x2 = 0 Move the constant term to the right: Add '2.416666667' to each side of the equation. -2.416666667 + -1.708333333x + 2.416666667 + x2 = 0 + 2.416666667 Reorder the terms: -2.416666667 + 2.416666667 + -1.708333333x + x2 = 0 + 2.416666667 Combine like terms: -2.416666667 + 2.416666667 = 0.000000000 0.000000000 + -1.708333333x + x2 = 0 + 2.416666667 -1.708333333x + x2 = 0 + 2.416666667 Combine like terms: 0 + 2.416666667 = 2.416666667 -1.708333333x + x2 = 2.416666667 The x term is -1.708333333x. Take half its coefficient (-0.8541666665). Square it (0.7296006942) and add it to both sides. Add '0.7296006942' to each side of the equation. -1.708333333x + 0.7296006942 + x2 = 2.416666667 + 0.7296006942 Reorder the terms: 0.7296006942 + -1.708333333x + x2 = 2.416666667 + 0.7296006942 Combine like terms: 2.416666667 + 0.7296006942 = 3.1462673612 0.7296006942 + -1.708333333x + x2 = 3.1462673612 Factor a perfect square on the left side: (x + -0.8541666665)(x + -0.8541666665) = 3.1462673612 Calculate the square root of the right side: 1.773772071 Break this problem into two subproblems by setting (x + -0.8541666665) equal to 1.773772071 and -1.773772071.Subproblem 1
x + -0.8541666665 = 1.773772071 Simplifying x + -0.8541666665 = 1.773772071 Reorder the terms: -0.8541666665 + x = 1.773772071 Solving -0.8541666665 + x = 1.773772071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8541666665' to each side of the equation. -0.8541666665 + 0.8541666665 + x = 1.773772071 + 0.8541666665 Combine like terms: -0.8541666665 + 0.8541666665 = 0.0000000000 0.0000000000 + x = 1.773772071 + 0.8541666665 x = 1.773772071 + 0.8541666665 Combine like terms: 1.773772071 + 0.8541666665 = 2.6279387375 x = 2.6279387375 Simplifying x = 2.6279387375Subproblem 2
x + -0.8541666665 = -1.773772071 Simplifying x + -0.8541666665 = -1.773772071 Reorder the terms: -0.8541666665 + x = -1.773772071 Solving -0.8541666665 + x = -1.773772071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.8541666665' to each side of the equation. -0.8541666665 + 0.8541666665 + x = -1.773772071 + 0.8541666665 Combine like terms: -0.8541666665 + 0.8541666665 = 0.0000000000 0.0000000000 + x = -1.773772071 + 0.8541666665 x = -1.773772071 + 0.8541666665 Combine like terms: -1.773772071 + 0.8541666665 = -0.9196054045 x = -0.9196054045 Simplifying x = -0.9196054045Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.6279387375, -0.9196054045}
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