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Simplifying 65.46x2 + 10.87x + -9.87 = 0 Reorder the terms: -9.87 + 10.87x + 65.46x2 = 0 Solving -9.87 + 10.87x + 65.46x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 65.46 the coefficient of the squared term: Divide each side by '65.46'. -0.1507791017 + 0.1660556065x + x2 = 0 Move the constant term to the right: Add '0.1507791017' to each side of the equation. -0.1507791017 + 0.1660556065x + 0.1507791017 + x2 = 0 + 0.1507791017 Reorder the terms: -0.1507791017 + 0.1507791017 + 0.1660556065x + x2 = 0 + 0.1507791017 Combine like terms: -0.1507791017 + 0.1507791017 = 0.0000000000 0.0000000000 + 0.1660556065x + x2 = 0 + 0.1507791017 0.1660556065x + x2 = 0 + 0.1507791017 Combine like terms: 0 + 0.1507791017 = 0.1507791017 0.1660556065x + x2 = 0.1507791017 The x term is 0.1660556065x. Take half its coefficient (0.08302780325). Square it (0.006893616113) and add it to both sides. Add '0.006893616113' to each side of the equation. 0.1660556065x + 0.006893616113 + x2 = 0.1507791017 + 0.006893616113 Reorder the terms: 0.006893616113 + 0.1660556065x + x2 = 0.1507791017 + 0.006893616113 Combine like terms: 0.1507791017 + 0.006893616113 = 0.157672717813 0.006893616113 + 0.1660556065x + x2 = 0.157672717813 Factor a perfect square on the left side: (x + 0.08302780325)(x + 0.08302780325) = 0.157672717813 Calculate the square root of the right side: 0.397080241 Break this problem into two subproblems by setting (x + 0.08302780325) equal to 0.397080241 and -0.397080241.Subproblem 1
x + 0.08302780325 = 0.397080241 Simplifying x + 0.08302780325 = 0.397080241 Reorder the terms: 0.08302780325 + x = 0.397080241 Solving 0.08302780325 + x = 0.397080241 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08302780325' to each side of the equation. 0.08302780325 + -0.08302780325 + x = 0.397080241 + -0.08302780325 Combine like terms: 0.08302780325 + -0.08302780325 = 0.00000000000 0.00000000000 + x = 0.397080241 + -0.08302780325 x = 0.397080241 + -0.08302780325 Combine like terms: 0.397080241 + -0.08302780325 = 0.31405243775 x = 0.31405243775 Simplifying x = 0.31405243775Subproblem 2
x + 0.08302780325 = -0.397080241 Simplifying x + 0.08302780325 = -0.397080241 Reorder the terms: 0.08302780325 + x = -0.397080241 Solving 0.08302780325 + x = -0.397080241 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.08302780325' to each side of the equation. 0.08302780325 + -0.08302780325 + x = -0.397080241 + -0.08302780325 Combine like terms: 0.08302780325 + -0.08302780325 = 0.00000000000 0.00000000000 + x = -0.397080241 + -0.08302780325 x = -0.397080241 + -0.08302780325 Combine like terms: -0.397080241 + -0.08302780325 = -0.48010804425 x = -0.48010804425 Simplifying x = -0.48010804425Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.31405243775, -0.48010804425}
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