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Simplifying 6x2 + -17x + 13 = 29x2 + -32 Reorder the terms: 13 + -17x + 6x2 = 29x2 + -32 Reorder the terms: 13 + -17x + 6x2 = -32 + 29x2 Solving 13 + -17x + 6x2 = -32 + 29x2 Solving for variable 'x'. Reorder the terms: 13 + 32 + -17x + 6x2 + -29x2 = -32 + 29x2 + 32 + -29x2 Combine like terms: 13 + 32 = 45 45 + -17x + 6x2 + -29x2 = -32 + 29x2 + 32 + -29x2 Combine like terms: 6x2 + -29x2 = -23x2 45 + -17x + -23x2 = -32 + 29x2 + 32 + -29x2 Reorder the terms: 45 + -17x + -23x2 = -32 + 32 + 29x2 + -29x2 Combine like terms: -32 + 32 = 0 45 + -17x + -23x2 = 0 + 29x2 + -29x2 45 + -17x + -23x2 = 29x2 + -29x2 Combine like terms: 29x2 + -29x2 = 0 45 + -17x + -23x2 = 0 Begin completing the square. Divide all terms by -23 the coefficient of the squared term: Divide each side by '-23'. -1.956521739 + 0.7391304348x + x2 = 0 Move the constant term to the right: Add '1.956521739' to each side of the equation. -1.956521739 + 0.7391304348x + 1.956521739 + x2 = 0 + 1.956521739 Reorder the terms: -1.956521739 + 1.956521739 + 0.7391304348x + x2 = 0 + 1.956521739 Combine like terms: -1.956521739 + 1.956521739 = 0.000000000 0.000000000 + 0.7391304348x + x2 = 0 + 1.956521739 0.7391304348x + x2 = 0 + 1.956521739 Combine like terms: 0 + 1.956521739 = 1.956521739 0.7391304348x + x2 = 1.956521739 The x term is 0.7391304348x. Take half its coefficient (0.3695652174). Square it (0.1365784499) and add it to both sides. Add '0.1365784499' to each side of the equation. 0.7391304348x + 0.1365784499 + x2 = 1.956521739 + 0.1365784499 Reorder the terms: 0.1365784499 + 0.7391304348x + x2 = 1.956521739 + 0.1365784499 Combine like terms: 1.956521739 + 0.1365784499 = 2.0931001889 0.1365784499 + 0.7391304348x + x2 = 2.0931001889 Factor a perfect square on the left side: (x + 0.3695652174)(x + 0.3695652174) = 2.0931001889 Calculate the square root of the right side: 1.446755055 Break this problem into two subproblems by setting (x + 0.3695652174) equal to 1.446755055 and -1.446755055.Subproblem 1
x + 0.3695652174 = 1.446755055 Simplifying x + 0.3695652174 = 1.446755055 Reorder the terms: 0.3695652174 + x = 1.446755055 Solving 0.3695652174 + x = 1.446755055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3695652174' to each side of the equation. 0.3695652174 + -0.3695652174 + x = 1.446755055 + -0.3695652174 Combine like terms: 0.3695652174 + -0.3695652174 = 0.0000000000 0.0000000000 + x = 1.446755055 + -0.3695652174 x = 1.446755055 + -0.3695652174 Combine like terms: 1.446755055 + -0.3695652174 = 1.0771898376 x = 1.0771898376 Simplifying x = 1.0771898376Subproblem 2
x + 0.3695652174 = -1.446755055 Simplifying x + 0.3695652174 = -1.446755055 Reorder the terms: 0.3695652174 + x = -1.446755055 Solving 0.3695652174 + x = -1.446755055 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3695652174' to each side of the equation. 0.3695652174 + -0.3695652174 + x = -1.446755055 + -0.3695652174 Combine like terms: 0.3695652174 + -0.3695652174 = 0.0000000000 0.0000000000 + x = -1.446755055 + -0.3695652174 x = -1.446755055 + -0.3695652174 Combine like terms: -1.446755055 + -0.3695652174 = -1.8163202724 x = -1.8163202724 Simplifying x = -1.8163202724Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0771898376, -1.8163202724}
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