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Simplifying 20x4 + -20x2 + 3 = 0 Reorder the terms: 3 + -20x2 + 20x4 = 0 Solving 3 + -20x2 + 20x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.15 + -1x2 + x4 = 0 Move the constant term to the right: Add '-0.15' to each side of the equation. 0.15 + -1x2 + -0.15 + x4 = 0 + -0.15 Reorder the terms: 0.15 + -0.15 + -1x2 + x4 = 0 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + -1x2 + x4 = 0 + -0.15 -1x2 + x4 = 0 + -0.15 Combine like terms: 0 + -0.15 = -0.15 -1x2 + x4 = -0.15 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 = -0.15 + 0.25 Reorder the terms: 0.25 + -1x2 + x4 = -0.15 + 0.25 Combine like terms: -0.15 + 0.25 = 0.1 0.25 + -1x2 + x4 = 0.1 Factor a perfect square on the left side: (x2 + -0.5)(x2 + -0.5) = 0.1 Calculate the square root of the right side: 0.316227766 Break this problem into two subproblems by setting (x2 + -0.5) equal to 0.316227766 and -0.316227766.Subproblem 1
x2 + -0.5 = 0.316227766 Simplifying x2 + -0.5 = 0.316227766 Reorder the terms: -0.5 + x2 = 0.316227766 Solving -0.5 + x2 = 0.316227766 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 = 0.316227766 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = 0.316227766 + 0.5 x2 = 0.316227766 + 0.5 Combine like terms: 0.316227766 + 0.5 = 0.816227766 x2 = 0.816227766 Simplifying x2 = 0.816227766 Take the square root of each side: x = {-0.903453245, 0.903453245}Subproblem 2
x2 + -0.5 = -0.316227766 Simplifying x2 + -0.5 = -0.316227766 Reorder the terms: -0.5 + x2 = -0.316227766 Solving -0.5 + x2 = -0.316227766 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 = -0.316227766 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x2 = -0.316227766 + 0.5 x2 = -0.316227766 + 0.5 Combine like terms: -0.316227766 + 0.5 = 0.183772234 x2 = 0.183772234 Simplifying x2 = 0.183772234 Take the square root of each side: x = {-0.428686638, 0.428686638}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.903453245, 0.903453245, -0.428686638, 0.428686638}
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