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Simplifying 2.4x2 + 1.3x + -5.2 = 0 Reorder the terms: -5.2 + 1.3x + 2.4x2 = 0 Solving -5.2 + 1.3x + 2.4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.4 the coefficient of the squared term: Divide each side by '2.4'. -2.166666667 + 0.5416666667x + x2 = 0 Move the constant term to the right: Add '2.166666667' to each side of the equation. -2.166666667 + 0.5416666667x + 2.166666667 + x2 = 0 + 2.166666667 Reorder the terms: -2.166666667 + 2.166666667 + 0.5416666667x + x2 = 0 + 2.166666667 Combine like terms: -2.166666667 + 2.166666667 = 0.000000000 0.000000000 + 0.5416666667x + x2 = 0 + 2.166666667 0.5416666667x + x2 = 0 + 2.166666667 Combine like terms: 0 + 2.166666667 = 2.166666667 0.5416666667x + x2 = 2.166666667 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 = 2.166666667 + 0.07335069448 Reorder the terms: 0.07335069448 + 0.5416666667x + x2 = 2.166666667 + 0.07335069448 Combine like terms: 2.166666667 + 0.07335069448 = 2.24001736148 0.07335069448 + 0.5416666667x + x2 = 2.24001736148 Factor a perfect square on the left side: (x + 0.2708333334)(x + 0.2708333334) = 2.24001736148 Calculate the square root of the right side: 1.496668755 Break this problem into two subproblems by setting (x + 0.2708333334) equal to 1.496668755 and -1.496668755.Subproblem 1
x + 0.2708333334 = 1.496668755 Simplifying x + 0.2708333334 = 1.496668755 Reorder the terms: 0.2708333334 + x = 1.496668755 Solving 0.2708333334 + x = 1.496668755 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 = 1.496668755 + -0.2708333334 Combine like terms: 0.2708333334 + -0.2708333334 = 0.0000000000 0.0000000000 + x = 1.496668755 + -0.2708333334 x = 1.496668755 + -0.2708333334 Combine like terms: 1.496668755 + -0.2708333334 = 1.2258354216 x = 1.2258354216 Simplifying x = 1.2258354216Subproblem 2
x + 0.2708333334 = -1.496668755 Simplifying x + 0.2708333334 = -1.496668755 Reorder the terms: 0.2708333334 + x = -1.496668755 Solving 0.2708333334 + x = -1.496668755 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 = -1.496668755 + -0.2708333334 Combine like terms: 0.2708333334 + -0.2708333334 = 0.0000000000 0.0000000000 + x = -1.496668755 + -0.2708333334 x = -1.496668755 + -0.2708333334 Combine like terms: -1.496668755 + -0.2708333334 = -1.7675020884 x = -1.7675020884 Simplifying x = -1.7675020884Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.2258354216, -1.7675020884}
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