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Simplifying 97x2 + -2x + -1 = 0 Reorder the terms: -1 + -2x + 97x2 = 0 Solving -1 + -2x + 97x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 97 the coefficient of the squared term: Divide each side by '97'. -0.01030927835 + -0.0206185567x + x2 = 0 Move the constant term to the right: Add '0.01030927835' to each side of the equation. -0.01030927835 + -0.0206185567x + 0.01030927835 + x2 = 0 + 0.01030927835 Reorder the terms: -0.01030927835 + 0.01030927835 + -0.0206185567x + x2 = 0 + 0.01030927835 Combine like terms: -0.01030927835 + 0.01030927835 = 0.00000000000 0.00000000000 + -0.0206185567x + x2 = 0 + 0.01030927835 -0.0206185567x + x2 = 0 + 0.01030927835 Combine like terms: 0 + 0.01030927835 = 0.01030927835 -0.0206185567x + x2 = 0.01030927835 The x term is -0.0206185567x. Take half its coefficient (-0.01030927835). Square it (0.0001062812201) and add it to both sides. Add '0.0001062812201' to each side of the equation. -0.0206185567x + 0.0001062812201 + x2 = 0.01030927835 + 0.0001062812201 Reorder the terms: 0.0001062812201 + -0.0206185567x + x2 = 0.01030927835 + 0.0001062812201 Combine like terms: 0.01030927835 + 0.0001062812201 = 0.0104155595701 0.0001062812201 + -0.0206185567x + x2 = 0.0104155595701 Factor a perfect square on the left side: (x + -0.01030927835)(x + -0.01030927835) = 0.0104155595701 Calculate the square root of the right side: 0.102056649 Break this problem into two subproblems by setting (x + -0.01030927835) equal to 0.102056649 and -0.102056649.Subproblem 1
x + -0.01030927835 = 0.102056649 Simplifying x + -0.01030927835 = 0.102056649 Reorder the terms: -0.01030927835 + x = 0.102056649 Solving -0.01030927835 + x = 0.102056649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01030927835' to each side of the equation. -0.01030927835 + 0.01030927835 + x = 0.102056649 + 0.01030927835 Combine like terms: -0.01030927835 + 0.01030927835 = 0.00000000000 0.00000000000 + x = 0.102056649 + 0.01030927835 x = 0.102056649 + 0.01030927835 Combine like terms: 0.102056649 + 0.01030927835 = 0.11236592735 x = 0.11236592735 Simplifying x = 0.11236592735Subproblem 2
x + -0.01030927835 = -0.102056649 Simplifying x + -0.01030927835 = -0.102056649 Reorder the terms: -0.01030927835 + x = -0.102056649 Solving -0.01030927835 + x = -0.102056649 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.01030927835' to each side of the equation. -0.01030927835 + 0.01030927835 + x = -0.102056649 + 0.01030927835 Combine like terms: -0.01030927835 + 0.01030927835 = 0.00000000000 0.00000000000 + x = -0.102056649 + 0.01030927835 x = -0.102056649 + 0.01030927835 Combine like terms: -0.102056649 + 0.01030927835 = -0.09174737065 x = -0.09174737065 Simplifying x = -0.09174737065Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.11236592735, -0.09174737065}
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