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Simplifying 69x2 + 27x + 2 = 0 Reorder the terms: 2 + 27x + 69x2 = 0 Solving 2 + 27x + 69x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 69 the coefficient of the squared term: Divide each side by '69'. 0.02898550725 + 0.3913043478x + x2 = 0 Move the constant term to the right: Add '-0.02898550725' to each side of the equation. 0.02898550725 + 0.3913043478x + -0.02898550725 + x2 = 0 + -0.02898550725 Reorder the terms: 0.02898550725 + -0.02898550725 + 0.3913043478x + x2 = 0 + -0.02898550725 Combine like terms: 0.02898550725 + -0.02898550725 = 0.00000000000 0.00000000000 + 0.3913043478x + x2 = 0 + -0.02898550725 0.3913043478x + x2 = 0 + -0.02898550725 Combine like terms: 0 + -0.02898550725 = -0.02898550725 0.3913043478x + x2 = -0.02898550725 The x term is 0.3913043478x. Take half its coefficient (0.1956521739). Square it (0.03827977315) and add it to both sides. Add '0.03827977315' to each side of the equation. 0.3913043478x + 0.03827977315 + x2 = -0.02898550725 + 0.03827977315 Reorder the terms: 0.03827977315 + 0.3913043478x + x2 = -0.02898550725 + 0.03827977315 Combine like terms: -0.02898550725 + 0.03827977315 = 0.0092942659 0.03827977315 + 0.3913043478x + x2 = 0.0092942659 Factor a perfect square on the left side: (x + 0.1956521739)(x + 0.1956521739) = 0.0092942659 Calculate the square root of the right side: 0.096406773 Break this problem into two subproblems by setting (x + 0.1956521739) equal to 0.096406773 and -0.096406773.Subproblem 1
x + 0.1956521739 = 0.096406773 Simplifying x + 0.1956521739 = 0.096406773 Reorder the terms: 0.1956521739 + x = 0.096406773 Solving 0.1956521739 + x = 0.096406773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1956521739' to each side of the equation. 0.1956521739 + -0.1956521739 + x = 0.096406773 + -0.1956521739 Combine like terms: 0.1956521739 + -0.1956521739 = 0.0000000000 0.0000000000 + x = 0.096406773 + -0.1956521739 x = 0.096406773 + -0.1956521739 Combine like terms: 0.096406773 + -0.1956521739 = -0.0992454009 x = -0.0992454009 Simplifying x = -0.0992454009Subproblem 2
x + 0.1956521739 = -0.096406773 Simplifying x + 0.1956521739 = -0.096406773 Reorder the terms: 0.1956521739 + x = -0.096406773 Solving 0.1956521739 + x = -0.096406773 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1956521739' to each side of the equation. 0.1956521739 + -0.1956521739 + x = -0.096406773 + -0.1956521739 Combine like terms: 0.1956521739 + -0.1956521739 = 0.0000000000 0.0000000000 + x = -0.096406773 + -0.1956521739 x = -0.096406773 + -0.1956521739 Combine like terms: -0.096406773 + -0.1956521739 = -0.2920589469 x = -0.2920589469 Simplifying x = -0.2920589469Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.0992454009, -0.2920589469}
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