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Simplifying 6.286x4 + -6.286x2 + 1 = 0 Reorder the terms: 1 + -6.286x2 + 6.286x4 = 0 Solving 1 + -6.286x2 + 6.286x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6.286 the coefficient of the squared term: Divide each side by '6.286'. 0.159083678 + -1x2 + x4 = 0 Move the constant term to the right: Add '-0.159083678' to each side of the equation. 0.159083678 + -1x2 + -0.159083678 + x4 = 0 + -0.159083678 Reorder the terms: 0.159083678 + -0.159083678 + -1x2 + x4 = 0 + -0.159083678 Combine like terms: 0.159083678 + -0.159083678 = 0.000000000 0.000000000 + -1x2 + x4 = 0 + -0.159083678 -1x2 + x4 = 0 + -0.159083678 Combine like terms: 0 + -0.159083678 = -0.159083678 -1x2 + x4 = -0.159083678 The x term is -1x2. 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. -1x2 + 0.25 + x4 = -0.159083678 + 0.25 Reorder the terms: 0.25 + -1x2 + x4 = -0.159083678 + 0.25 Combine like terms: -0.159083678 + 0.25 = 0.090916322 0.25 + -1x2 + x4 = 0.090916322 Factor a perfect square on the left side: (x2 + -0.5)(x2 + -0.5) = 0.090916322 Calculate the square root of the right side: 0.301523336 Break this problem into two subproblems by setting (x2 + -0.5) equal to 0.301523336 and -0.301523336.Subproblem 1
x2 + -0.5 = 0.301523336 Simplifying x2 + -0.5 = 0.301523336 Reorder the terms: -0.5 + x2 = 0.301523336 Solving -0.5 + x2 = 0.301523336 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 + x2 = 0.301523336 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 0.301523336 + 0.5 x2 = 0.301523336 + 0.5 Combine like terms: 0.301523336 + 0.5 = 0.801523336 x2 = 0.801523336 Simplifying x2 = 0.801523336 Take the square root of each side: x = {-0.895278357, 0.895278357}Subproblem 2
x2 + -0.5 = -0.301523336 Simplifying x2 + -0.5 = -0.301523336 Reorder the terms: -0.5 + x2 = -0.301523336 Solving -0.5 + x2 = -0.301523336 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 + x2 = -0.301523336 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -0.301523336 + 0.5 x2 = -0.301523336 + 0.5 Combine like terms: -0.301523336 + 0.5 = 0.198476664 x2 = 0.198476664 Simplifying x2 = 0.198476664 Take the square root of each side: x = {-0.445507199, 0.445507199}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.895278357, 0.895278357, -0.445507199, 0.445507199}
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