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Simplifying 94x2 + 201x + 81 = 0 Reorder the terms: 81 + 201x + 94x2 = 0 Solving 81 + 201x + 94x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 94 the coefficient of the squared term: Divide each side by '94'. 0.8617021277 + 2.138297872x + x2 = 0 Move the constant term to the right: Add '-0.8617021277' to each side of the equation. 0.8617021277 + 2.138297872x + -0.8617021277 + x2 = 0 + -0.8617021277 Reorder the terms: 0.8617021277 + -0.8617021277 + 2.138297872x + x2 = 0 + -0.8617021277 Combine like terms: 0.8617021277 + -0.8617021277 = 0.0000000000 0.0000000000 + 2.138297872x + x2 = 0 + -0.8617021277 2.138297872x + x2 = 0 + -0.8617021277 Combine like terms: 0 + -0.8617021277 = -0.8617021277 2.138297872x + x2 = -0.8617021277 The x term is 2.138297872x. Take half its coefficient (1.069148936). Square it (1.143079447) and add it to both sides. Add '1.143079447' to each side of the equation. 2.138297872x + 1.143079447 + x2 = -0.8617021277 + 1.143079447 Reorder the terms: 1.143079447 + 2.138297872x + x2 = -0.8617021277 + 1.143079447 Combine like terms: -0.8617021277 + 1.143079447 = 0.2813773193 1.143079447 + 2.138297872x + x2 = 0.2813773193 Factor a perfect square on the left side: (x + 1.069148936)(x + 1.069148936) = 0.2813773193 Calculate the square root of the right side: 0.53045011 Break this problem into two subproblems by setting (x + 1.069148936) equal to 0.53045011 and -0.53045011.Subproblem 1
x + 1.069148936 = 0.53045011 Simplifying x + 1.069148936 = 0.53045011 Reorder the terms: 1.069148936 + x = 0.53045011 Solving 1.069148936 + x = 0.53045011 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.069148936' to each side of the equation. 1.069148936 + -1.069148936 + x = 0.53045011 + -1.069148936 Combine like terms: 1.069148936 + -1.069148936 = 0.000000000 0.000000000 + x = 0.53045011 + -1.069148936 x = 0.53045011 + -1.069148936 Combine like terms: 0.53045011 + -1.069148936 = -0.538698826 x = -0.538698826 Simplifying x = -0.538698826Subproblem 2
x + 1.069148936 = -0.53045011 Simplifying x + 1.069148936 = -0.53045011 Reorder the terms: 1.069148936 + x = -0.53045011 Solving 1.069148936 + x = -0.53045011 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.069148936' to each side of the equation. 1.069148936 + -1.069148936 + x = -0.53045011 + -1.069148936 Combine like terms: 1.069148936 + -1.069148936 = 0.000000000 0.000000000 + x = -0.53045011 + -1.069148936 x = -0.53045011 + -1.069148936 Combine like terms: -0.53045011 + -1.069148936 = -1.599599046 x = -1.599599046 Simplifying x = -1.599599046Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.538698826, -1.599599046}
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