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Simplifying 23x2 + -75x + 50 = 0 Reorder the terms: 50 + -75x + 23x2 = 0 Solving 50 + -75x + 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'. 2.173913043 + -3.260869565x + x2 = 0 Move the constant term to the right: Add '-2.173913043' to each side of the equation. 2.173913043 + -3.260869565x + -2.173913043 + x2 = 0 + -2.173913043 Reorder the terms: 2.173913043 + -2.173913043 + -3.260869565x + x2 = 0 + -2.173913043 Combine like terms: 2.173913043 + -2.173913043 = 0.000000000 0.000000000 + -3.260869565x + x2 = 0 + -2.173913043 -3.260869565x + x2 = 0 + -2.173913043 Combine like terms: 0 + -2.173913043 = -2.173913043 -3.260869565x + x2 = -2.173913043 The x term is -3.260869565x. Take half its coefficient (-1.630434783). Square it (2.658317582) and add it to both sides. Add '2.658317582' to each side of the equation. -3.260869565x + 2.658317582 + x2 = -2.173913043 + 2.658317582 Reorder the terms: 2.658317582 + -3.260869565x + x2 = -2.173913043 + 2.658317582 Combine like terms: -2.173913043 + 2.658317582 = 0.484404539 2.658317582 + -3.260869565x + x2 = 0.484404539 Factor a perfect square on the left side: (x + -1.630434783)(x + -1.630434783) = 0.484404539 Calculate the square root of the right side: 0.695991766 Break this problem into two subproblems by setting (x + -1.630434783) equal to 0.695991766 and -0.695991766.Subproblem 1
x + -1.630434783 = 0.695991766 Simplifying x + -1.630434783 = 0.695991766 Reorder the terms: -1.630434783 + x = 0.695991766 Solving -1.630434783 + x = 0.695991766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.630434783' to each side of the equation. -1.630434783 + 1.630434783 + x = 0.695991766 + 1.630434783 Combine like terms: -1.630434783 + 1.630434783 = 0.000000000 0.000000000 + x = 0.695991766 + 1.630434783 x = 0.695991766 + 1.630434783 Combine like terms: 0.695991766 + 1.630434783 = 2.326426549 x = 2.326426549 Simplifying x = 2.326426549Subproblem 2
x + -1.630434783 = -0.695991766 Simplifying x + -1.630434783 = -0.695991766 Reorder the terms: -1.630434783 + x = -0.695991766 Solving -1.630434783 + x = -0.695991766 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.630434783' to each side of the equation. -1.630434783 + 1.630434783 + x = -0.695991766 + 1.630434783 Combine like terms: -1.630434783 + 1.630434783 = 0.000000000 0.000000000 + x = -0.695991766 + 1.630434783 x = -0.695991766 + 1.630434783 Combine like terms: -0.695991766 + 1.630434783 = 0.934443017 x = 0.934443017 Simplifying x = 0.934443017Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.326426549, 0.934443017}
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