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Simplifying (2x + 9) + x = 460x2 Reorder the terms: (9 + 2x) + x = 460x2 Remove parenthesis around (9 + 2x) 9 + 2x + x = 460x2 Combine like terms: 2x + x = 3x 9 + 3x = 460x2 Solving 9 + 3x = 460x2 Solving for variable 'x'. Combine like terms: 460x2 + -460x2 = 0 9 + 3x + -460x2 = 0 Begin completing the square. Divide all terms by -460 the coefficient of the squared term: Divide each side by '-460'. -0.01956521739 + -0.00652173913x + x2 = 0 Move the constant term to the right: Add '0.01956521739' to each side of the equation. -0.01956521739 + -0.00652173913x + 0.01956521739 + x2 = 0 + 0.01956521739 Reorder the terms: -0.01956521739 + 0.01956521739 + -0.00652173913x + x2 = 0 + 0.01956521739 Combine like terms: -0.01956521739 + 0.01956521739 = 0.00000000000 0.00000000000 + -0.00652173913x + x2 = 0 + 0.01956521739 -0.00652173913x + x2 = 0 + 0.01956521739 Combine like terms: 0 + 0.01956521739 = 0.01956521739 -0.00652173913x + x2 = 0.01956521739 The x term is -0.00652173913x. Take half its coefficient (-0.003260869565). Square it (0.00001063327032) and add it to both sides. Add '0.00001063327032' to each side of the equation. -0.00652173913x + 0.00001063327032 + x2 = 0.01956521739 + 0.00001063327032 Reorder the terms: 0.00001063327032 + -0.00652173913x + x2 = 0.01956521739 + 0.00001063327032 Combine like terms: 0.01956521739 + 0.00001063327032 = 0.01957585066032 0.00001063327032 + -0.00652173913x + x2 = 0.01957585066032 Factor a perfect square on the left side: (x + -0.003260869565)(x + -0.003260869565) = 0.01957585066032 Calculate the square root of the right side: 0.139913726 Break this problem into two subproblems by setting (x + -0.003260869565) equal to 0.139913726 and -0.139913726.Subproblem 1
x + -0.003260869565 = 0.139913726 Simplifying x + -0.003260869565 = 0.139913726 Reorder the terms: -0.003260869565 + x = 0.139913726 Solving -0.003260869565 + x = 0.139913726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.003260869565' to each side of the equation. -0.003260869565 + 0.003260869565 + x = 0.139913726 + 0.003260869565 Combine like terms: -0.003260869565 + 0.003260869565 = 0.000000000000 0.000000000000 + x = 0.139913726 + 0.003260869565 x = 0.139913726 + 0.003260869565 Combine like terms: 0.139913726 + 0.003260869565 = 0.143174595565 x = 0.143174595565 Simplifying x = 0.143174595565Subproblem 2
x + -0.003260869565 = -0.139913726 Simplifying x + -0.003260869565 = -0.139913726 Reorder the terms: -0.003260869565 + x = -0.139913726 Solving -0.003260869565 + x = -0.139913726 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.003260869565' to each side of the equation. -0.003260869565 + 0.003260869565 + x = -0.139913726 + 0.003260869565 Combine like terms: -0.003260869565 + 0.003260869565 = 0.000000000000 0.000000000000 + x = -0.139913726 + 0.003260869565 x = -0.139913726 + 0.003260869565 Combine like terms: -0.139913726 + 0.003260869565 = -0.136652856435 x = -0.136652856435 Simplifying x = -0.136652856435Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.143174595565, -0.136652856435}
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