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Simplifying (106x2) + 6x + -102 = 0 Reorder the terms: -102 + 6x + (106x2) = 0 Solving -102 + 6x + (106x2) = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-51 + 3x + (53x2)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-51 + 3x + (53x2))' equal to zero and attempt to solve: Simplifying -51 + 3x + (53x2) = 0 Solving -51 + 3x + (53x2) = 0 Begin completing the square. Divide all terms by 53 the coefficient of the squared term: Divide each side by '53'. -0.9622641509 + 0.05660377358x + x2 = 0 Move the constant term to the right: Add '0.9622641509' to each side of the equation. -0.9622641509 + 0.05660377358x + 0.9622641509 + x2 = 0 + 0.9622641509 Reorder the terms: -0.9622641509 + 0.9622641509 + 0.05660377358x + x2 = 0 + 0.9622641509 Combine like terms: -0.9622641509 + 0.9622641509 = 0.0000000000 0.0000000000 + 0.05660377358x + x2 = 0 + 0.9622641509 0.05660377358x + x2 = 0 + 0.9622641509 Combine like terms: 0 + 0.9622641509 = 0.9622641509 0.05660377358x + x2 = 0.9622641509 The x term is 0.05660377358x. Take half its coefficient (0.02830188679). Square it (0.0008009967959) and add it to both sides. Add '0.0008009967959' to each side of the equation. 0.05660377358x + 0.0008009967959 + x2 = 0.9622641509 + 0.0008009967959 Reorder the terms: 0.0008009967959 + 0.05660377358x + x2 = 0.9622641509 + 0.0008009967959 Combine like terms: 0.9622641509 + 0.0008009967959 = 0.9630651476959 0.0008009967959 + 0.05660377358x + x2 = 0.9630651476959 Factor a perfect square on the left side: ((x) + 0.02830188679)((x) + 0.02830188679) = 0.9630651476959 Calculate the square root of the right side: 0.981358827 Break this problem into two subproblems by setting ((x) + 0.02830188679) equal to 0.981358827 and -0.981358827.Subproblem 1
(x) + 0.02830188679 = 0.981358827 Simplifying (x) + 0.02830188679 = 0.981358827 x + 0.02830188679 = 0.981358827 Reorder the terms: 0.02830188679 + x = 0.981358827 Solving 0.02830188679 + x = 0.981358827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02830188679' to each side of the equation. 0.02830188679 + -0.02830188679 + x = 0.981358827 + -0.02830188679 Combine like terms: 0.02830188679 + -0.02830188679 = 0.00000000000 0.00000000000 + x = 0.981358827 + -0.02830188679 x = 0.981358827 + -0.02830188679 Combine like terms: 0.981358827 + -0.02830188679 = 0.95305694021 x = 0.95305694021 Simplifying x = 0.95305694021Subproblem 2
(x) + 0.02830188679 = -0.981358827 Simplifying (x) + 0.02830188679 = -0.981358827 x + 0.02830188679 = -0.981358827 Reorder the terms: 0.02830188679 + x = -0.981358827 Solving 0.02830188679 + x = -0.981358827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.02830188679' to each side of the equation. 0.02830188679 + -0.02830188679 + x = -0.981358827 + -0.02830188679 Combine like terms: 0.02830188679 + -0.02830188679 = 0.00000000000 0.00000000000 + x = -0.981358827 + -0.02830188679 x = -0.981358827 + -0.02830188679 Combine like terms: -0.981358827 + -0.02830188679 = -1.00966071379 x = -1.00966071379 Simplifying x = -1.00966071379Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.95305694021, -1.00966071379}Solution
x = {0.95305694021, -1.00966071379}
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