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Simplifying 0.1111111x4 + -1.333333x2 + 3 = 0 Reorder the terms: 3 + -1.333333x2 + 0.1111111x4 = 0 Solving 3 + -1.333333x2 + 0.1111111x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.1111111 the coefficient of the squared term: Divide each side by '0.1111111'. 27.0000027 + -11.9999982x2 + x4 = 0 Move the constant term to the right: Add '-27.0000027' to each side of the equation. 27.0000027 + -11.9999982x2 + -27.0000027 + x4 = 0 + -27.0000027 Reorder the terms: 27.0000027 + -27.0000027 + -11.9999982x2 + x4 = 0 + -27.0000027 Combine like terms: 27.0000027 + -27.0000027 = 0.0000000 0.0000000 + -11.9999982x2 + x4 = 0 + -27.0000027 -11.9999982x2 + x4 = 0 + -27.0000027 Combine like terms: 0 + -27.0000027 = -27.0000027 -11.9999982x2 + x4 = -27.0000027 The x term is -11.9999982x2. Take half its coefficient (-5.9999991). Square it (35.99998920) and add it to both sides. Add '35.99998920' to each side of the equation. -11.9999982x2 + 35.99998920 + x4 = -27.0000027 + 35.99998920 Reorder the terms: 35.99998920 + -11.9999982x2 + x4 = -27.0000027 + 35.99998920 Combine like terms: -27.0000027 + 35.99998920 = 8.9999865 35.99998920 + -11.9999982x2 + x4 = 8.9999865 Factor a perfect square on the left side: (x2 + -5.9999991)(x2 + -5.9999991) = 8.9999865 Calculate the square root of the right side: 2.99999775 Break this problem into two subproblems by setting (x2 + -5.9999991) equal to 2.99999775 and -2.99999775.Subproblem 1
x2 + -5.9999991 = 2.99999775 Simplifying x2 + -5.9999991 = 2.99999775 Reorder the terms: -5.9999991 + x2 = 2.99999775 Solving -5.9999991 + x2 = 2.99999775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.9999991' to each side of the equation. -5.9999991 + 5.9999991 + x2 = 2.99999775 + 5.9999991 Combine like terms: -5.9999991 + 5.9999991 = 0.0000000 0.0000000 + x2 = 2.99999775 + 5.9999991 x2 = 2.99999775 + 5.9999991 Combine like terms: 2.99999775 + 5.9999991 = 8.99999685 x2 = 8.99999685 Simplifying x2 = 8.99999685 Take the square root of each side: x = {-2.999999475, 2.999999475}Subproblem 2
x2 + -5.9999991 = -2.99999775 Simplifying x2 + -5.9999991 = -2.99999775 Reorder the terms: -5.9999991 + x2 = -2.99999775 Solving -5.9999991 + x2 = -2.99999775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.9999991' to each side of the equation. -5.9999991 + 5.9999991 + x2 = -2.99999775 + 5.9999991 Combine like terms: -5.9999991 + 5.9999991 = 0.0000000 0.0000000 + x2 = -2.99999775 + 5.9999991 x2 = -2.99999775 + 5.9999991 Combine like terms: -2.99999775 + 5.9999991 = 3.00000135 x2 = 3.00000135 Simplifying x2 = 3.00000135 Take the square root of each side: x = {-1.732051197, 1.732051197}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.999999475, 2.999999475, -1.732051197, 1.732051197}
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