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Simplifying 0.0122x4 + 0.83x2 + -12.85 = 0 Reorder the terms: -12.85 + 0.83x2 + 0.0122x4 = 0 Solving -12.85 + 0.83x2 + 0.0122x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0122 the coefficient of the squared term: Divide each side by '0.0122'. -1053.278689 + 68.03278689x2 + x4 = 0 Move the constant term to the right: Add '1053.278689' to each side of the equation. -1053.278689 + 68.03278689x2 + 1053.278689 + x4 = 0 + 1053.278689 Reorder the terms: -1053.278689 + 1053.278689 + 68.03278689x2 + x4 = 0 + 1053.278689 Combine like terms: -1053.278689 + 1053.278689 = 0.000000 0.000000 + 68.03278689x2 + x4 = 0 + 1053.278689 68.03278689x2 + x4 = 0 + 1053.278689 Combine like terms: 0 + 1053.278689 = 1053.278689 68.03278689x2 + x4 = 1053.278689 The x term is 68.03278689x2. Take half its coefficient (34.01639345). Square it (1157.115023) and add it to both sides. Add '1157.115023' to each side of the equation. 68.03278689x2 + 1157.115023 + x4 = 1053.278689 + 1157.115023 Reorder the terms: 1157.115023 + 68.03278689x2 + x4 = 1053.278689 + 1157.115023 Combine like terms: 1053.278689 + 1157.115023 = 2210.393712 1157.115023 + 68.03278689x2 + x4 = 2210.393712 Factor a perfect square on the left side: (x2 + 34.01639345)(x2 + 34.01639345) = 2210.393712 Calculate the square root of the right side: 47.014824386 Break this problem into two subproblems by setting (x2 + 34.01639345) equal to 47.014824386 and -47.014824386.Subproblem 1
x2 + 34.01639345 = 47.014824386 Simplifying x2 + 34.01639345 = 47.014824386 Reorder the terms: 34.01639345 + x2 = 47.014824386 Solving 34.01639345 + x2 = 47.014824386 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34.01639345' to each side of the equation. 34.01639345 + -34.01639345 + x2 = 47.014824386 + -34.01639345 Combine like terms: 34.01639345 + -34.01639345 = 0.00000000 0.00000000 + x2 = 47.014824386 + -34.01639345 x2 = 47.014824386 + -34.01639345 Combine like terms: 47.014824386 + -34.01639345 = 12.998430936 x2 = 12.998430936 Simplifying x2 = 12.998430936 Take the square root of each side: x = {-3.605333679, 3.605333679}Subproblem 2
x2 + 34.01639345 = -47.014824386 Simplifying x2 + 34.01639345 = -47.014824386 Reorder the terms: 34.01639345 + x2 = -47.014824386 Solving 34.01639345 + x2 = -47.014824386 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34.01639345' to each side of the equation. 34.01639345 + -34.01639345 + x2 = -47.014824386 + -34.01639345 Combine like terms: 34.01639345 + -34.01639345 = 0.00000000 0.00000000 + x2 = -47.014824386 + -34.01639345 x2 = -47.014824386 + -34.01639345 Combine like terms: -47.014824386 + -34.01639345 = -81.031217836 x2 = -81.031217836 Simplifying x2 = -81.031217836 Reorder the terms: 81.031217836 + x2 = -81.031217836 + 81.031217836 Combine like terms: -81.031217836 + 81.031217836 = 0.000000000 81.031217836 + x2 = 0.000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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