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Simplifying 0 = -2.4x2 + 14.2x + 10 Reorder the terms: 0 = 10 + 14.2x + -2.4x2 Solving 0 = 10 + 14.2x + -2.4x2 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + -14.2x + 2.4x2 = 10 + 14.2x + -2.4x2 + -10 + -14.2x + 2.4x2 Reorder the terms: -10 + -14.2x + 2.4x2 = 10 + -10 + 14.2x + -14.2x + -2.4x2 + 2.4x2 Combine like terms: 10 + -10 = 0 -10 + -14.2x + 2.4x2 = 0 + 14.2x + -14.2x + -2.4x2 + 2.4x2 -10 + -14.2x + 2.4x2 = 14.2x + -14.2x + -2.4x2 + 2.4x2 Combine like terms: 14.2x + -14.2x = 0.0 -10 + -14.2x + 2.4x2 = 0.0 + -2.4x2 + 2.4x2 -10 + -14.2x + 2.4x2 = -2.4x2 + 2.4x2 Combine like terms: -2.4x2 + 2.4x2 = 0.0 -10 + -14.2x + 2.4x2 = 0.0 Begin completing the square. Divide all terms by 2.4 the coefficient of the squared term: Divide each side by '2.4'. -4.166666667 + -5.916666667x + x2 = 0 Move the constant term to the right: Add '4.166666667' to each side of the equation. -4.166666667 + -5.916666667x + 4.166666667 + x2 = 0 + 4.166666667 Reorder the terms: -4.166666667 + 4.166666667 + -5.916666667x + x2 = 0 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + -5.916666667x + x2 = 0 + 4.166666667 -5.916666667x + x2 = 0 + 4.166666667 Combine like terms: 0 + 4.166666667 = 4.166666667 -5.916666667x + x2 = 4.166666667 The x term is -5.916666667x. Take half its coefficient (-2.958333334). Square it (8.751736115) and add it to both sides. Add '8.751736115' to each side of the equation. -5.916666667x + 8.751736115 + x2 = 4.166666667 + 8.751736115 Reorder the terms: 8.751736115 + -5.916666667x + x2 = 4.166666667 + 8.751736115 Combine like terms: 4.166666667 + 8.751736115 = 12.918402782 8.751736115 + -5.916666667x + x2 = 12.918402782 Factor a perfect square on the left side: (x + -2.958333334)(x + -2.958333334) = 12.918402782 Calculate the square root of the right side: 3.594217965 Break this problem into two subproblems by setting (x + -2.958333334) equal to 3.594217965 and -3.594217965.Subproblem 1
x + -2.958333334 = 3.594217965 Simplifying x + -2.958333334 = 3.594217965 Reorder the terms: -2.958333334 + x = 3.594217965 Solving -2.958333334 + x = 3.594217965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.958333334' to each side of the equation. -2.958333334 + 2.958333334 + x = 3.594217965 + 2.958333334 Combine like terms: -2.958333334 + 2.958333334 = 0.000000000 0.000000000 + x = 3.594217965 + 2.958333334 x = 3.594217965 + 2.958333334 Combine like terms: 3.594217965 + 2.958333334 = 6.552551299 x = 6.552551299 Simplifying x = 6.552551299Subproblem 2
x + -2.958333334 = -3.594217965 Simplifying x + -2.958333334 = -3.594217965 Reorder the terms: -2.958333334 + x = -3.594217965 Solving -2.958333334 + x = -3.594217965 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.958333334' to each side of the equation. -2.958333334 + 2.958333334 + x = -3.594217965 + 2.958333334 Combine like terms: -2.958333334 + 2.958333334 = 0.000000000 0.000000000 + x = -3.594217965 + 2.958333334 x = -3.594217965 + 2.958333334 Combine like terms: -3.594217965 + 2.958333334 = -0.635884631 x = -0.635884631 Simplifying x = -0.635884631Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.552551299, -0.635884631}
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