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Simplifying 32x2 + 28x + 1 = 0 Reorder the terms: 1 + 28x + 32x2 = 0 Solving 1 + 28x + 32x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 32 the coefficient of the squared term: Divide each side by '32'. 0.03125 + 0.875x + x2 = 0 Move the constant term to the right: Add '-0.03125' to each side of the equation. 0.03125 + 0.875x + -0.03125 + x2 = 0 + -0.03125 Reorder the terms: 0.03125 + -0.03125 + 0.875x + x2 = 0 + -0.03125 Combine like terms: 0.03125 + -0.03125 = 0.00000 0.00000 + 0.875x + x2 = 0 + -0.03125 0.875x + x2 = 0 + -0.03125 Combine like terms: 0 + -0.03125 = -0.03125 0.875x + x2 = -0.03125 The x term is 0.875x. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875x + 0.19140625 + x2 = -0.03125 + 0.19140625 Reorder the terms: 0.19140625 + 0.875x + x2 = -0.03125 + 0.19140625 Combine like terms: -0.03125 + 0.19140625 = 0.16015625 0.19140625 + 0.875x + x2 = 0.16015625 Factor a perfect square on the left side: (x + 0.4375)(x + 0.4375) = 0.16015625 Calculate the square root of the right side: 0.400195265 Break this problem into two subproblems by setting (x + 0.4375) equal to 0.400195265 and -0.400195265.Subproblem 1
x + 0.4375 = 0.400195265 Simplifying x + 0.4375 = 0.400195265 Reorder the terms: 0.4375 + x = 0.400195265 Solving 0.4375 + x = 0.400195265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = 0.400195265 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = 0.400195265 + -0.4375 x = 0.400195265 + -0.4375 Combine like terms: 0.400195265 + -0.4375 = -0.037304735 x = -0.037304735 Simplifying x = -0.037304735Subproblem 2
x + 0.4375 = -0.400195265 Simplifying x + 0.4375 = -0.400195265 Reorder the terms: 0.4375 + x = -0.400195265 Solving 0.4375 + x = -0.400195265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = -0.400195265 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = -0.400195265 + -0.4375 x = -0.400195265 + -0.4375 Combine like terms: -0.400195265 + -0.4375 = -0.837695265 x = -0.837695265 Simplifying x = -0.837695265Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.037304735, -0.837695265}
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