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Simplifying 24x2 = 55x + 89 Reorder the terms: 24x2 = 89 + 55x Solving 24x2 = 89 + 55x Solving for variable 'x'. Reorder the terms: -89 + -55x + 24x2 = 89 + 55x + -89 + -55x Reorder the terms: -89 + -55x + 24x2 = 89 + -89 + 55x + -55x Combine like terms: 89 + -89 = 0 -89 + -55x + 24x2 = 0 + 55x + -55x -89 + -55x + 24x2 = 55x + -55x Combine like terms: 55x + -55x = 0 -89 + -55x + 24x2 = 0 Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -3.708333333 + -2.291666667x + x2 = 0 Move the constant term to the right: Add '3.708333333' to each side of the equation. -3.708333333 + -2.291666667x + 3.708333333 + x2 = 0 + 3.708333333 Reorder the terms: -3.708333333 + 3.708333333 + -2.291666667x + x2 = 0 + 3.708333333 Combine like terms: -3.708333333 + 3.708333333 = 0.000000000 0.000000000 + -2.291666667x + x2 = 0 + 3.708333333 -2.291666667x + x2 = 0 + 3.708333333 Combine like terms: 0 + 3.708333333 = 3.708333333 -2.291666667x + x2 = 3.708333333 The x term is -2.291666667x. Take half its coefficient (-1.145833334). Square it (1.312934029) and add it to both sides. Add '1.312934029' to each side of the equation. -2.291666667x + 1.312934029 + x2 = 3.708333333 + 1.312934029 Reorder the terms: 1.312934029 + -2.291666667x + x2 = 3.708333333 + 1.312934029 Combine like terms: 3.708333333 + 1.312934029 = 5.021267362 1.312934029 + -2.291666667x + x2 = 5.021267362 Factor a perfect square on the left side: (x + -1.145833334)(x + -1.145833334) = 5.021267362 Calculate the square root of the right side: 2.240818458 Break this problem into two subproblems by setting (x + -1.145833334) equal to 2.240818458 and -2.240818458.Subproblem 1
x + -1.145833334 = 2.240818458 Simplifying x + -1.145833334 = 2.240818458 Reorder the terms: -1.145833334 + x = 2.240818458 Solving -1.145833334 + x = 2.240818458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.145833334' to each side of the equation. -1.145833334 + 1.145833334 + x = 2.240818458 + 1.145833334 Combine like terms: -1.145833334 + 1.145833334 = 0.000000000 0.000000000 + x = 2.240818458 + 1.145833334 x = 2.240818458 + 1.145833334 Combine like terms: 2.240818458 + 1.145833334 = 3.386651792 x = 3.386651792 Simplifying x = 3.386651792Subproblem 2
x + -1.145833334 = -2.240818458 Simplifying x + -1.145833334 = -2.240818458 Reorder the terms: -1.145833334 + x = -2.240818458 Solving -1.145833334 + x = -2.240818458 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.145833334' to each side of the equation. -1.145833334 + 1.145833334 + x = -2.240818458 + 1.145833334 Combine like terms: -1.145833334 + 1.145833334 = 0.000000000 0.000000000 + x = -2.240818458 + 1.145833334 x = -2.240818458 + 1.145833334 Combine like terms: -2.240818458 + 1.145833334 = -1.094985124 x = -1.094985124 Simplifying x = -1.094985124Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.386651792, -1.094985124}
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