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Simplifying -23x2 + 112x + -96 = 0 Reorder the terms: -96 + 112x + -23x2 = 0 Solving -96 + 112x + -23x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -23 the coefficient of the squared term: Divide each side by '-23'. 4.173913043 + -4.869565217x + x2 = 0 Move the constant term to the right: Add '-4.173913043' to each side of the equation. 4.173913043 + -4.869565217x + -4.173913043 + x2 = 0 + -4.173913043 Reorder the terms: 4.173913043 + -4.173913043 + -4.869565217x + x2 = 0 + -4.173913043 Combine like terms: 4.173913043 + -4.173913043 = 0.000000000 0.000000000 + -4.869565217x + x2 = 0 + -4.173913043 -4.869565217x + x2 = 0 + -4.173913043 Combine like terms: 0 + -4.173913043 = -4.173913043 -4.869565217x + x2 = -4.173913043 The x term is -4.869565217x. Take half its coefficient (-2.434782609). Square it (5.928166353) and add it to both sides. Add '5.928166353' to each side of the equation. -4.869565217x + 5.928166353 + x2 = -4.173913043 + 5.928166353 Reorder the terms: 5.928166353 + -4.869565217x + x2 = -4.173913043 + 5.928166353 Combine like terms: -4.173913043 + 5.928166353 = 1.75425331 5.928166353 + -4.869565217x + x2 = 1.75425331 Factor a perfect square on the left side: (x + -2.434782609)(x + -2.434782609) = 1.75425331 Calculate the square root of the right side: 1.32448228 Break this problem into two subproblems by setting (x + -2.434782609) equal to 1.32448228 and -1.32448228.Subproblem 1
x + -2.434782609 = 1.32448228 Simplifying x + -2.434782609 = 1.32448228 Reorder the terms: -2.434782609 + x = 1.32448228 Solving -2.434782609 + x = 1.32448228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.434782609' to each side of the equation. -2.434782609 + 2.434782609 + x = 1.32448228 + 2.434782609 Combine like terms: -2.434782609 + 2.434782609 = 0.000000000 0.000000000 + x = 1.32448228 + 2.434782609 x = 1.32448228 + 2.434782609 Combine like terms: 1.32448228 + 2.434782609 = 3.759264889 x = 3.759264889 Simplifying x = 3.759264889Subproblem 2
x + -2.434782609 = -1.32448228 Simplifying x + -2.434782609 = -1.32448228 Reorder the terms: -2.434782609 + x = -1.32448228 Solving -2.434782609 + x = -1.32448228 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.434782609' to each side of the equation. -2.434782609 + 2.434782609 + x = -1.32448228 + 2.434782609 Combine like terms: -2.434782609 + 2.434782609 = 0.000000000 0.000000000 + x = -1.32448228 + 2.434782609 x = -1.32448228 + 2.434782609 Combine like terms: -1.32448228 + 2.434782609 = 1.110300329 x = 1.110300329 Simplifying x = 1.110300329Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.759264889, 1.110300329}
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