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Simplifying x4 + -17x2 + 18 = 0 Reorder the terms: 18 + -17x2 + x4 = 0 Solving 18 + -17x2 + x4 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-18' to each side of the equation. 18 + -17x2 + -18 + x4 = 0 + -18 Reorder the terms: 18 + -18 + -17x2 + x4 = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -17x2 + x4 = 0 + -18 -17x2 + x4 = 0 + -18 Combine like terms: 0 + -18 = -18 -17x2 + x4 = -18 The x term is -17x2. Take half its coefficient (-8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. -17x2 + 72.25 + x4 = -18 + 72.25 Reorder the terms: 72.25 + -17x2 + x4 = -18 + 72.25 Combine like terms: -18 + 72.25 = 54.25 72.25 + -17x2 + x4 = 54.25 Factor a perfect square on the left side: (x2 + -8.5)(x2 + -8.5) = 54.25 Calculate the square root of the right side: 7.365459931 Break this problem into two subproblems by setting (x2 + -8.5) equal to 7.365459931 and -7.365459931.Subproblem 1
x2 + -8.5 = 7.365459931 Simplifying x2 + -8.5 = 7.365459931 Reorder the terms: -8.5 + x2 = 7.365459931 Solving -8.5 + x2 = 7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x2 = 7.365459931 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x2 = 7.365459931 + 8.5 x2 = 7.365459931 + 8.5 Combine like terms: 7.365459931 + 8.5 = 15.865459931 x2 = 15.865459931 Simplifying x2 = 15.865459931 Take the square root of each side: x = {-3.983146988, 3.983146988}Subproblem 2
x2 + -8.5 = -7.365459931 Simplifying x2 + -8.5 = -7.365459931 Reorder the terms: -8.5 + x2 = -7.365459931 Solving -8.5 + x2 = -7.365459931 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.5' to each side of the equation. -8.5 + 8.5 + x2 = -7.365459931 + 8.5 Combine like terms: -8.5 + 8.5 = 0.0 0.0 + x2 = -7.365459931 + 8.5 x2 = -7.365459931 + 8.5 Combine like terms: -7.365459931 + 8.5 = 1.134540069 x2 = 1.134540069 Simplifying x2 = 1.134540069 Take the square root of each side: x = {-1.065147909, 1.065147909}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.983146988, 3.983146988, -1.065147909, 1.065147909}
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