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Simplifying 32x2 + 128x + -1 = 0 Reorder the terms: -1 + 128x + 32x2 = 0 Solving -1 + 128x + 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 + 4x + x2 = 0 Move the constant term to the right: Add '0.03125' to each side of the equation. -0.03125 + 4x + 0.03125 + x2 = 0 + 0.03125 Reorder the terms: -0.03125 + 0.03125 + 4x + x2 = 0 + 0.03125 Combine like terms: -0.03125 + 0.03125 = 0.00000 0.00000 + 4x + x2 = 0 + 0.03125 4x + x2 = 0 + 0.03125 Combine like terms: 0 + 0.03125 = 0.03125 4x + x2 = 0.03125 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 0.03125 + 4 Reorder the terms: 4 + 4x + x2 = 0.03125 + 4 Combine like terms: 0.03125 + 4 = 4.03125 4 + 4x + x2 = 4.03125 Factor a perfect square on the left side: (x + 2)(x + 2) = 4.03125 Calculate the square root of the right side: 2.007797301 Break this problem into two subproblems by setting (x + 2) equal to 2.007797301 and -2.007797301.Subproblem 1
x + 2 = 2.007797301 Simplifying x + 2 = 2.007797301 Reorder the terms: 2 + x = 2.007797301 Solving 2 + x = 2.007797301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 2.007797301 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.007797301 + -2 x = 2.007797301 + -2 Combine like terms: 2.007797301 + -2 = 0.007797301 x = 0.007797301 Simplifying x = 0.007797301Subproblem 2
x + 2 = -2.007797301 Simplifying x + 2 = -2.007797301 Reorder the terms: 2 + x = -2.007797301 Solving 2 + x = -2.007797301 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -2.007797301 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.007797301 + -2 x = -2.007797301 + -2 Combine like terms: -2.007797301 + -2 = -4.007797301 x = -4.007797301 Simplifying x = -4.007797301Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.007797301, -4.007797301}
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