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Simplifying 40.9x4 + -80.8381x2 = -39.9 Reorder the terms: -80.8381x2 + 40.9x4 = -39.9 Solving -80.8381x2 + 40.9x4 = -39.9 Solving for variable 'x'. Reorder the terms: 39.9 + -80.8381x2 + 40.9x4 = -39.9 + 39.9 Combine like terms: -39.9 + 39.9 = 0.0 39.9 + -80.8381x2 + 40.9x4 = 0.0 Begin completing the square. Divide all terms by 40.9 the coefficient of the squared term: Divide each side by '40.9'. 0.9755501222 + -1.976481663x2 + x4 = 0 Move the constant term to the right: Add '-0.9755501222' to each side of the equation. 0.9755501222 + -1.976481663x2 + -0.9755501222 + x4 = 0 + -0.9755501222 Reorder the terms: 0.9755501222 + -0.9755501222 + -1.976481663x2 + x4 = 0 + -0.9755501222 Combine like terms: 0.9755501222 + -0.9755501222 = 0.0000000000 0.0000000000 + -1.976481663x2 + x4 = 0 + -0.9755501222 -1.976481663x2 + x4 = 0 + -0.9755501222 Combine like terms: 0 + -0.9755501222 = -0.9755501222 -1.976481663x2 + x4 = -0.9755501222 The x term is -1.976481663x2. Take half its coefficient (-0.9882408315). Square it (0.9766199410) and add it to both sides. Add '0.9766199410' to each side of the equation. -1.976481663x2 + 0.9766199410 + x4 = -0.9755501222 + 0.9766199410 Reorder the terms: 0.9766199410 + -1.976481663x2 + x4 = -0.9755501222 + 0.9766199410 Combine like terms: -0.9755501222 + 0.9766199410 = 0.0010698188 0.9766199410 + -1.976481663x2 + x4 = 0.0010698188 Factor a perfect square on the left side: (x2 + -0.9882408315)(x2 + -0.9882408315) = 0.0010698188 Calculate the square root of the right side: 0.032708085 Break this problem into two subproblems by setting (x2 + -0.9882408315) equal to 0.032708085 and -0.032708085.Subproblem 1
x2 + -0.9882408315 = 0.032708085 Simplifying x2 + -0.9882408315 = 0.032708085 Reorder the terms: -0.9882408315 + x2 = 0.032708085 Solving -0.9882408315 + x2 = 0.032708085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9882408315' to each side of the equation. -0.9882408315 + 0.9882408315 + x2 = 0.032708085 + 0.9882408315 Combine like terms: -0.9882408315 + 0.9882408315 = 0.0000000000 0.0000000000 + x2 = 0.032708085 + 0.9882408315 x2 = 0.032708085 + 0.9882408315 Combine like terms: 0.032708085 + 0.9882408315 = 1.0209489165 x2 = 1.0209489165 Simplifying x2 = 1.0209489165 Take the square root of each side: x = {-1.010420168, 1.010420168}Subproblem 2
x2 + -0.9882408315 = -0.032708085 Simplifying x2 + -0.9882408315 = -0.032708085 Reorder the terms: -0.9882408315 + x2 = -0.032708085 Solving -0.9882408315 + x2 = -0.032708085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9882408315' to each side of the equation. -0.9882408315 + 0.9882408315 + x2 = -0.032708085 + 0.9882408315 Combine like terms: -0.9882408315 + 0.9882408315 = 0.0000000000 0.0000000000 + x2 = -0.032708085 + 0.9882408315 x2 = -0.032708085 + 0.9882408315 Combine like terms: -0.032708085 + 0.9882408315 = 0.9555327465 x2 = 0.9555327465 Simplifying x2 = 0.9555327465 Take the square root of each side: x = {-0.977513553, 0.977513553}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.010420168, 1.010420168, -0.977513553, 0.977513553}
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