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Simplifying 3x4 + -9x2 + 2 = 0 Reorder the terms: 2 + -9x2 + 3x4 = 0 Solving 2 + -9x2 + 3x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 0.6666666667 + -3x2 + x4 = 0 Move the constant term to the right: Add '-0.6666666667' to each side of the equation. 0.6666666667 + -3x2 + -0.6666666667 + x4 = 0 + -0.6666666667 Reorder the terms: 0.6666666667 + -0.6666666667 + -3x2 + x4 = 0 + -0.6666666667 Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000 0.0000000000 + -3x2 + x4 = 0 + -0.6666666667 -3x2 + x4 = 0 + -0.6666666667 Combine like terms: 0 + -0.6666666667 = -0.6666666667 -3x2 + x4 = -0.6666666667 The x term is -3x2. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x2 + 2.25 + x4 = -0.6666666667 + 2.25 Reorder the terms: 2.25 + -3x2 + x4 = -0.6666666667 + 2.25 Combine like terms: -0.6666666667 + 2.25 = 1.5833333333 2.25 + -3x2 + x4 = 1.5833333333 Factor a perfect square on the left side: (x2 + -1.5)(x2 + -1.5) = 1.5833333333 Calculate the square root of the right side: 1.258305739 Break this problem into two subproblems by setting (x2 + -1.5) equal to 1.258305739 and -1.258305739.Subproblem 1
x2 + -1.5 = 1.258305739 Simplifying x2 + -1.5 = 1.258305739 Reorder the terms: -1.5 + x2 = 1.258305739 Solving -1.5 + x2 = 1.258305739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = 1.258305739 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = 1.258305739 + 1.5 x2 = 1.258305739 + 1.5 Combine like terms: 1.258305739 + 1.5 = 2.758305739 x2 = 2.758305739 Simplifying x2 = 2.758305739 Take the square root of each side: x = {-1.660814782, 1.660814782}Subproblem 2
x2 + -1.5 = -1.258305739 Simplifying x2 + -1.5 = -1.258305739 Reorder the terms: -1.5 + x2 = -1.258305739 Solving -1.5 + x2 = -1.258305739 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x2 = -1.258305739 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x2 = -1.258305739 + 1.5 x2 = -1.258305739 + 1.5 Combine like terms: -1.258305739 + 1.5 = 0.241694261 x2 = 0.241694261 Simplifying x2 = 0.241694261 Take the square root of each side: x = {-0.491624105, 0.491624105}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.660814782, 1.660814782, -0.491624105, 0.491624105}
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