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Simplifying (4x2) + -4x + -1 = 0 Reorder the terms: -1 + -4x + (4x2) = 0 Solving -1 + -4x + (4x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -1x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -1x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -1x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -1x + x2 = 0 + 0.25 -1x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -1x + x2 = 0.25 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.25 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.25 + 0.25 Combine like terms: 0.25 + 0.25 = 0.5 0.25 + -1x + x2 = 0.5 Factor a perfect square on the left side: ((x) + -0.5)((x) + -0.5) = 0.5 Calculate the square root of the right side: 0.707106781 Break this problem into two subproblems by setting ((x) + -0.5) equal to 0.707106781 and -0.707106781.Subproblem 1
(x) + -0.5 = 0.707106781 Simplifying (x) + -0.5 = 0.707106781 x + -0.5 = 0.707106781 Reorder the terms: -0.5 + x = 0.707106781 Solving -0.5 + x = 0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.707106781 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.707106781 + 0.5 x = 0.707106781 + 0.5 Combine like terms: 0.707106781 + 0.5 = 1.207106781 x = 1.207106781 Simplifying x = 1.207106781Subproblem 2
(x) + -0.5 = -0.707106781 Simplifying (x) + -0.5 = -0.707106781 x + -0.5 = -0.707106781 Reorder the terms: -0.5 + x = -0.707106781 Solving -0.5 + x = -0.707106781 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.707106781 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.707106781 + 0.5 x = -0.707106781 + 0.5 Combine like terms: -0.707106781 + 0.5 = -0.207106781 x = -0.207106781 Simplifying x = -0.207106781Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.207106781, -0.207106781}
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