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Simplifying 3x4 + -27x2 + 50 = 0 Reorder the terms: 50 + -27x2 + 3x4 = 0 Solving 50 + -27x2 + 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'. 16.66666667 + -9x2 + x4 = 0 Move the constant term to the right: Add '-16.66666667' to each side of the equation. 16.66666667 + -9x2 + -16.66666667 + x4 = 0 + -16.66666667 Reorder the terms: 16.66666667 + -16.66666667 + -9x2 + x4 = 0 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + -9x2 + x4 = 0 + -16.66666667 -9x2 + x4 = 0 + -16.66666667 Combine like terms: 0 + -16.66666667 = -16.66666667 -9x2 + x4 = -16.66666667 The x term is -9x2. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x2 + 20.25 + x4 = -16.66666667 + 20.25 Reorder the terms: 20.25 + -9x2 + x4 = -16.66666667 + 20.25 Combine like terms: -16.66666667 + 20.25 = 3.58333333 20.25 + -9x2 + x4 = 3.58333333 Factor a perfect square on the left side: (x2 + -4.5)(x2 + -4.5) = 3.58333333 Calculate the square root of the right side: 1.892969448 Break this problem into two subproblems by setting (x2 + -4.5) equal to 1.892969448 and -1.892969448.Subproblem 1
x2 + -4.5 = 1.892969448 Simplifying x2 + -4.5 = 1.892969448 Reorder the terms: -4.5 + x2 = 1.892969448 Solving -4.5 + x2 = 1.892969448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x2 = 1.892969448 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = 1.892969448 + 4.5 x2 = 1.892969448 + 4.5 Combine like terms: 1.892969448 + 4.5 = 6.392969448 x2 = 6.392969448 Simplifying x2 = 6.392969448 Take the square root of each side: x = {-2.528432211, 2.528432211}Subproblem 2
x2 + -4.5 = -1.892969448 Simplifying x2 + -4.5 = -1.892969448 Reorder the terms: -4.5 + x2 = -1.892969448 Solving -4.5 + x2 = -1.892969448 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x2 = -1.892969448 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x2 = -1.892969448 + 4.5 x2 = -1.892969448 + 4.5 Combine like terms: -1.892969448 + 4.5 = 2.607030552 x2 = 2.607030552 Simplifying x2 = 2.607030552 Take the square root of each side: x = {-1.61463016, 1.61463016}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.528432211, 2.528432211, -1.61463016, 1.61463016}
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