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Simplifying x = 24x2 + -12x + -72 Reorder the terms: x = -72 + -12x + 24x2 Solving x = -72 + -12x + 24x2 Solving for variable 'x'. Reorder the terms: 72 + x + 12x + -24x2 = -72 + -12x + 24x2 + 72 + 12x + -24x2 Combine like terms: x + 12x = 13x 72 + 13x + -24x2 = -72 + -12x + 24x2 + 72 + 12x + -24x2 Reorder the terms: 72 + 13x + -24x2 = -72 + 72 + -12x + 12x + 24x2 + -24x2 Combine like terms: -72 + 72 = 0 72 + 13x + -24x2 = 0 + -12x + 12x + 24x2 + -24x2 72 + 13x + -24x2 = -12x + 12x + 24x2 + -24x2 Combine like terms: -12x + 12x = 0 72 + 13x + -24x2 = 0 + 24x2 + -24x2 72 + 13x + -24x2 = 24x2 + -24x2 Combine like terms: 24x2 + -24x2 = 0 72 + 13x + -24x2 = 0 Begin completing the square. Divide all terms by -24 the coefficient of the squared term: Divide each side by '-24'. -3 + -0.5416666667x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -0.5416666667x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -0.5416666667x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -0.5416666667x + x2 = 0 + 3 -0.5416666667x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -0.5416666667x + x2 = 3 The x term is -0.5416666667x. Take half its coefficient (-0.2708333334). Square it (0.07335069448) and add it to both sides. Add '0.07335069448' to each side of the equation. -0.5416666667x + 0.07335069448 + x2 = 3 + 0.07335069448 Reorder the terms: 0.07335069448 + -0.5416666667x + x2 = 3 + 0.07335069448 Combine like terms: 3 + 0.07335069448 = 3.07335069448 0.07335069448 + -0.5416666667x + x2 = 3.07335069448 Factor a perfect square on the left side: (x + -0.2708333334)(x + -0.2708333334) = 3.07335069448 Calculate the square root of the right side: 1.753097457 Break this problem into two subproblems by setting (x + -0.2708333334) equal to 1.753097457 and -1.753097457.Subproblem 1
x + -0.2708333334 = 1.753097457 Simplifying x + -0.2708333334 = 1.753097457 Reorder the terms: -0.2708333334 + x = 1.753097457 Solving -0.2708333334 + x = 1.753097457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2708333334' to each side of the equation. -0.2708333334 + 0.2708333334 + x = 1.753097457 + 0.2708333334 Combine like terms: -0.2708333334 + 0.2708333334 = 0.0000000000 0.0000000000 + x = 1.753097457 + 0.2708333334 x = 1.753097457 + 0.2708333334 Combine like terms: 1.753097457 + 0.2708333334 = 2.0239307904 x = 2.0239307904 Simplifying x = 2.0239307904Subproblem 2
x + -0.2708333334 = -1.753097457 Simplifying x + -0.2708333334 = -1.753097457 Reorder the terms: -0.2708333334 + x = -1.753097457 Solving -0.2708333334 + x = -1.753097457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2708333334' to each side of the equation. -0.2708333334 + 0.2708333334 + x = -1.753097457 + 0.2708333334 Combine like terms: -0.2708333334 + 0.2708333334 = 0.0000000000 0.0000000000 + x = -1.753097457 + 0.2708333334 x = -1.753097457 + 0.2708333334 Combine like terms: -1.753097457 + 0.2708333334 = -1.4822641236 x = -1.4822641236 Simplifying x = -1.4822641236Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.0239307904, -1.4822641236}
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