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Simplifying 23x + 3.50x2 + -117.72 = 235.44 Reorder the terms: -117.72 + 23x + 3.50x2 = 235.44 Solving -117.72 + 23x + 3.50x2 = 235.44 Solving for variable 'x'. Reorder the terms: -117.72 + -235.44 + 23x + 3.50x2 = 235.44 + -235.44 Combine like terms: -117.72 + -235.44 = -353.16 -353.16 + 23x + 3.50x2 = 235.44 + -235.44 Combine like terms: 235.44 + -235.44 = 0.00 -353.16 + 23x + 3.50x2 = 0.00 Begin completing the square. Divide all terms by 3.50 the coefficient of the squared term: Divide each side by '3.50'. -100.9028571 + 6.571428571x + x2 = 0 Move the constant term to the right: Add '100.9028571' to each side of the equation. -100.9028571 + 6.571428571x + 100.9028571 + x2 = 0 + 100.9028571 Reorder the terms: -100.9028571 + 100.9028571 + 6.571428571x + x2 = 0 + 100.9028571 Combine like terms: -100.9028571 + 100.9028571 = 0.0000000 0.0000000 + 6.571428571x + x2 = 0 + 100.9028571 6.571428571x + x2 = 0 + 100.9028571 Combine like terms: 0 + 100.9028571 = 100.9028571 6.571428571x + x2 = 100.9028571 The x term is 6.571428571x. Take half its coefficient (3.285714286). Square it (10.79591837) and add it to both sides. Add '10.79591837' to each side of the equation. 6.571428571x + 10.79591837 + x2 = 100.9028571 + 10.79591837 Reorder the terms: 10.79591837 + 6.571428571x + x2 = 100.9028571 + 10.79591837 Combine like terms: 100.9028571 + 10.79591837 = 111.69877547 10.79591837 + 6.571428571x + x2 = 111.69877547 Factor a perfect square on the left side: (x + 3.285714286)(x + 3.285714286) = 111.69877547 Calculate the square root of the right side: 10.568764141 Break this problem into two subproblems by setting (x + 3.285714286) equal to 10.568764141 and -10.568764141.Subproblem 1
x + 3.285714286 = 10.568764141 Simplifying x + 3.285714286 = 10.568764141 Reorder the terms: 3.285714286 + x = 10.568764141 Solving 3.285714286 + x = 10.568764141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.285714286' to each side of the equation. 3.285714286 + -3.285714286 + x = 10.568764141 + -3.285714286 Combine like terms: 3.285714286 + -3.285714286 = 0.000000000 0.000000000 + x = 10.568764141 + -3.285714286 x = 10.568764141 + -3.285714286 Combine like terms: 10.568764141 + -3.285714286 = 7.283049855 x = 7.283049855 Simplifying x = 7.283049855Subproblem 2
x + 3.285714286 = -10.568764141 Simplifying x + 3.285714286 = -10.568764141 Reorder the terms: 3.285714286 + x = -10.568764141 Solving 3.285714286 + x = -10.568764141 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.285714286' to each side of the equation. 3.285714286 + -3.285714286 + x = -10.568764141 + -3.285714286 Combine like terms: 3.285714286 + -3.285714286 = 0.000000000 0.000000000 + x = -10.568764141 + -3.285714286 x = -10.568764141 + -3.285714286 Combine like terms: -10.568764141 + -3.285714286 = -13.854478427 x = -13.854478427 Simplifying x = -13.854478427Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.283049855, -13.854478427}
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