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Simplifying 59x2 + -13x + -30 = 0 Reorder the terms: -30 + -13x + 59x2 = 0 Solving -30 + -13x + 59x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 59 the coefficient of the squared term: Divide each side by '59'. -0.5084745763 + -0.2203389831x + x2 = 0 Move the constant term to the right: Add '0.5084745763' to each side of the equation. -0.5084745763 + -0.2203389831x + 0.5084745763 + x2 = 0 + 0.5084745763 Reorder the terms: -0.5084745763 + 0.5084745763 + -0.2203389831x + x2 = 0 + 0.5084745763 Combine like terms: -0.5084745763 + 0.5084745763 = 0.0000000000 0.0000000000 + -0.2203389831x + x2 = 0 + 0.5084745763 -0.2203389831x + x2 = 0 + 0.5084745763 Combine like terms: 0 + 0.5084745763 = 0.5084745763 -0.2203389831x + x2 = 0.5084745763 The x term is -0.2203389831x. Take half its coefficient (-0.1101694916). Square it (0.01213731688) and add it to both sides. Add '0.01213731688' to each side of the equation. -0.2203389831x + 0.01213731688 + x2 = 0.5084745763 + 0.01213731688 Reorder the terms: 0.01213731688 + -0.2203389831x + x2 = 0.5084745763 + 0.01213731688 Combine like terms: 0.5084745763 + 0.01213731688 = 0.52061189318 0.01213731688 + -0.2203389831x + x2 = 0.52061189318 Factor a perfect square on the left side: (x + -0.1101694916)(x + -0.1101694916) = 0.52061189318 Calculate the square root of the right side: 0.721534402 Break this problem into two subproblems by setting (x + -0.1101694916) equal to 0.721534402 and -0.721534402.Subproblem 1
x + -0.1101694916 = 0.721534402 Simplifying x + -0.1101694916 = 0.721534402 Reorder the terms: -0.1101694916 + x = 0.721534402 Solving -0.1101694916 + x = 0.721534402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1101694916' to each side of the equation. -0.1101694916 + 0.1101694916 + x = 0.721534402 + 0.1101694916 Combine like terms: -0.1101694916 + 0.1101694916 = 0.0000000000 0.0000000000 + x = 0.721534402 + 0.1101694916 x = 0.721534402 + 0.1101694916 Combine like terms: 0.721534402 + 0.1101694916 = 0.8317038936 x = 0.8317038936 Simplifying x = 0.8317038936Subproblem 2
x + -0.1101694916 = -0.721534402 Simplifying x + -0.1101694916 = -0.721534402 Reorder the terms: -0.1101694916 + x = -0.721534402 Solving -0.1101694916 + x = -0.721534402 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1101694916' to each side of the equation. -0.1101694916 + 0.1101694916 + x = -0.721534402 + 0.1101694916 Combine like terms: -0.1101694916 + 0.1101694916 = 0.0000000000 0.0000000000 + x = -0.721534402 + 0.1101694916 x = -0.721534402 + 0.1101694916 Combine like terms: -0.721534402 + 0.1101694916 = -0.6113649104 x = -0.6113649104 Simplifying x = -0.6113649104Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8317038936, -0.6113649104}
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