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Simplifying 2x + 34x2 + -322 = 0 Reorder the terms: -322 + 2x + 34x2 = 0 Solving -322 + 2x + 34x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-161 + x + 17x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-161 + x + 17x2)' equal to zero and attempt to solve: Simplifying -161 + x + 17x2 = 0 Solving -161 + x + 17x2 = 0 Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -9.470588235 + 0.05882352941x + x2 = 0 Move the constant term to the right: Add '9.470588235' to each side of the equation. -9.470588235 + 0.05882352941x + 9.470588235 + x2 = 0 + 9.470588235 Reorder the terms: -9.470588235 + 9.470588235 + 0.05882352941x + x2 = 0 + 9.470588235 Combine like terms: -9.470588235 + 9.470588235 = 0.000000000 0.000000000 + 0.05882352941x + x2 = 0 + 9.470588235 0.05882352941x + x2 = 0 + 9.470588235 Combine like terms: 0 + 9.470588235 = 9.470588235 0.05882352941x + x2 = 9.470588235 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.05882352941x + 0.25 + x2 = 9.470588235 + 0.25 Reorder the terms: 0.25 + 0.05882352941x + x2 = 9.470588235 + 0.25 Combine like terms: 9.470588235 + 0.25 = 9.720588235 0.25 + 0.05882352941x + x2 = 9.720588235 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 9.720588235 Calculate the square root of the right side: 3.11778579 Break this problem into two subproblems by setting (x + 0.5) equal to 3.11778579 and -3.11778579.Subproblem 1
x + 0.5 = 3.11778579 Simplifying x + 0.5 = 3.11778579 Reorder the terms: 0.5 + x = 3.11778579 Solving 0.5 + x = 3.11778579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 3.11778579 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 3.11778579 + -0.5 x = 3.11778579 + -0.5 Combine like terms: 3.11778579 + -0.5 = 2.61778579 x = 2.61778579 Simplifying x = 2.61778579Subproblem 2
x + 0.5 = -3.11778579 Simplifying x + 0.5 = -3.11778579 Reorder the terms: 0.5 + x = -3.11778579 Solving 0.5 + x = -3.11778579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -3.11778579 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -3.11778579 + -0.5 x = -3.11778579 + -0.5 Combine like terms: -3.11778579 + -0.5 = -3.61778579 x = -3.61778579 Simplifying x = -3.61778579Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.61778579, -3.61778579}Solution
x = {2.61778579, -3.61778579}
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