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Simplifying 36x2 + 2.44948974278x + -1 = 0 Reorder the terms: -1 + 2.44948974278x + 36x2 = 0 Solving -1 + 2.44948974278x + 36x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 36 the coefficient of the squared term: Divide each side by '36'. -0.02777777778 + 0.06804138174x + x2 = 0 Move the constant term to the right: Add '0.02777777778' to each side of the equation. -0.02777777778 + 0.06804138174x + 0.02777777778 + x2 = 0 + 0.02777777778 Reorder the terms: -0.02777777778 + 0.02777777778 + 0.06804138174x + x2 = 0 + 0.02777777778 Combine like terms: -0.02777777778 + 0.02777777778 = 0.00000000000 0.00000000000 + 0.06804138174x + x2 = 0 + 0.02777777778 0.06804138174x + x2 = 0 + 0.02777777778 Combine like terms: 0 + 0.02777777778 = 0.02777777778 0.06804138174x + x2 = 0.02777777778 The x term is 0.06804138174x. Take half its coefficient (0.03402069087). Square it (0.001157407407) and add it to both sides. Add '0.001157407407' to each side of the equation. 0.06804138174x + 0.001157407407 + x2 = 0.02777777778 + 0.001157407407 Reorder the terms: 0.001157407407 + 0.06804138174x + x2 = 0.02777777778 + 0.001157407407 Combine like terms: 0.02777777778 + 0.001157407407 = 0.028935185187 0.001157407407 + 0.06804138174x + x2 = 0.028935185187 Factor a perfect square on the left side: (x + 0.03402069087)(x + 0.03402069087) = 0.028935185187 Calculate the square root of the right side: 0.170103454 Break this problem into two subproblems by setting (x + 0.03402069087) equal to 0.170103454 and -0.170103454.Subproblem 1
x + 0.03402069087 = 0.170103454 Simplifying x + 0.03402069087 = 0.170103454 Reorder the terms: 0.03402069087 + x = 0.170103454 Solving 0.03402069087 + x = 0.170103454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03402069087' to each side of the equation. 0.03402069087 + -0.03402069087 + x = 0.170103454 + -0.03402069087 Combine like terms: 0.03402069087 + -0.03402069087 = 0.00000000000 0.00000000000 + x = 0.170103454 + -0.03402069087 x = 0.170103454 + -0.03402069087 Combine like terms: 0.170103454 + -0.03402069087 = 0.13608276313 x = 0.13608276313 Simplifying x = 0.13608276313Subproblem 2
x + 0.03402069087 = -0.170103454 Simplifying x + 0.03402069087 = -0.170103454 Reorder the terms: 0.03402069087 + x = -0.170103454 Solving 0.03402069087 + x = -0.170103454 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03402069087' to each side of the equation. 0.03402069087 + -0.03402069087 + x = -0.170103454 + -0.03402069087 Combine like terms: 0.03402069087 + -0.03402069087 = 0.00000000000 0.00000000000 + x = -0.170103454 + -0.03402069087 x = -0.170103454 + -0.03402069087 Combine like terms: -0.170103454 + -0.03402069087 = -0.20412414487 x = -0.20412414487 Simplifying x = -0.20412414487Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.13608276313, -0.20412414487}
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