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Simplifying 3x4 + -33x2 + 56 = 0 Reorder the terms: 56 + -33x2 + 3x4 = 0 Solving 56 + -33x2 + 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'. 18.66666667 + -11x2 + x4 = 0 Move the constant term to the right: Add '-18.66666667' to each side of the equation. 18.66666667 + -11x2 + -18.66666667 + x4 = 0 + -18.66666667 Reorder the terms: 18.66666667 + -18.66666667 + -11x2 + x4 = 0 + -18.66666667 Combine like terms: 18.66666667 + -18.66666667 = 0.00000000 0.00000000 + -11x2 + x4 = 0 + -18.66666667 -11x2 + x4 = 0 + -18.66666667 Combine like terms: 0 + -18.66666667 = -18.66666667 -11x2 + x4 = -18.66666667 The x term is -11x2. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x2 + 30.25 + x4 = -18.66666667 + 30.25 Reorder the terms: 30.25 + -11x2 + x4 = -18.66666667 + 30.25 Combine like terms: -18.66666667 + 30.25 = 11.58333333 30.25 + -11x2 + x4 = 11.58333333 Factor a perfect square on the left side: (x2 + -5.5)(x2 + -5.5) = 11.58333333 Calculate the square root of the right side: 3.403429642 Break this problem into two subproblems by setting (x2 + -5.5) equal to 3.403429642 and -3.403429642.Subproblem 1
x2 + -5.5 = 3.403429642 Simplifying x2 + -5.5 = 3.403429642 Reorder the terms: -5.5 + x2 = 3.403429642 Solving -5.5 + x2 = 3.403429642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x2 = 3.403429642 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x2 = 3.403429642 + 5.5 x2 = 3.403429642 + 5.5 Combine like terms: 3.403429642 + 5.5 = 8.903429642 x2 = 8.903429642 Simplifying x2 = 8.903429642 Take the square root of each side: x = {-2.983861532, 2.983861532}Subproblem 2
x2 + -5.5 = -3.403429642 Simplifying x2 + -5.5 = -3.403429642 Reorder the terms: -5.5 + x2 = -3.403429642 Solving -5.5 + x2 = -3.403429642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x2 = -3.403429642 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x2 = -3.403429642 + 5.5 x2 = -3.403429642 + 5.5 Combine like terms: -3.403429642 + 5.5 = 2.096570358 x2 = 2.096570358 Simplifying x2 = 2.096570358 Take the square root of each side: x = {-1.447953852, 1.447953852}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.983861532, 2.983861532, -1.447953852, 1.447953852}
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