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Simplifying 9x2 + -50x + 46 = 0 Reorder the terms: 46 + -50x + 9x2 = 0 Solving 46 + -50x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 5.111111111 + -5.555555556x + x2 = 0 Move the constant term to the right: Add '-5.111111111' to each side of the equation. 5.111111111 + -5.555555556x + -5.111111111 + x2 = 0 + -5.111111111 Reorder the terms: 5.111111111 + -5.111111111 + -5.555555556x + x2 = 0 + -5.111111111 Combine like terms: 5.111111111 + -5.111111111 = 0.000000000 0.000000000 + -5.555555556x + x2 = 0 + -5.111111111 -5.555555556x + x2 = 0 + -5.111111111 Combine like terms: 0 + -5.111111111 = -5.111111111 -5.555555556x + x2 = -5.111111111 The x term is -5.555555556x. Take half its coefficient (-2.777777778). Square it (7.716049384) and add it to both sides. Add '7.716049384' to each side of the equation. -5.555555556x + 7.716049384 + x2 = -5.111111111 + 7.716049384 Reorder the terms: 7.716049384 + -5.555555556x + x2 = -5.111111111 + 7.716049384 Combine like terms: -5.111111111 + 7.716049384 = 2.604938273 7.716049384 + -5.555555556x + x2 = 2.604938273 Factor a perfect square on the left side: (x + -2.777777778)(x + -2.777777778) = 2.604938273 Calculate the square root of the right side: 1.613982117 Break this problem into two subproblems by setting (x + -2.777777778) equal to 1.613982117 and -1.613982117.Subproblem 1
x + -2.777777778 = 1.613982117 Simplifying x + -2.777777778 = 1.613982117 Reorder the terms: -2.777777778 + x = 1.613982117 Solving -2.777777778 + x = 1.613982117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.777777778' to each side of the equation. -2.777777778 + 2.777777778 + x = 1.613982117 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + x = 1.613982117 + 2.777777778 x = 1.613982117 + 2.777777778 Combine like terms: 1.613982117 + 2.777777778 = 4.391759895 x = 4.391759895 Simplifying x = 4.391759895Subproblem 2
x + -2.777777778 = -1.613982117 Simplifying x + -2.777777778 = -1.613982117 Reorder the terms: -2.777777778 + x = -1.613982117 Solving -2.777777778 + x = -1.613982117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.777777778' to each side of the equation. -2.777777778 + 2.777777778 + x = -1.613982117 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + x = -1.613982117 + 2.777777778 x = -1.613982117 + 2.777777778 Combine like terms: -1.613982117 + 2.777777778 = 1.163795661 x = 1.163795661 Simplifying x = 1.163795661Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.391759895, 1.163795661}
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