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Simplifying 3x4 + -37x2 + 36 = 0 Reorder the terms: 36 + -37x2 + 3x4 = 0 Solving 36 + -37x2 + 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'. 12 + -12.33333333x2 + x4 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -12.33333333x2 + -12 + x4 = 0 + -12 Reorder the terms: 12 + -12 + -12.33333333x2 + x4 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -12.33333333x2 + x4 = 0 + -12 -12.33333333x2 + x4 = 0 + -12 Combine like terms: 0 + -12 = -12 -12.33333333x2 + x4 = -12 The x term is -12.33333333x2. Take half its coefficient (-6.166666665). Square it (38.02777776) and add it to both sides. Add '38.02777776' to each side of the equation. -12.33333333x2 + 38.02777776 + x4 = -12 + 38.02777776 Reorder the terms: 38.02777776 + -12.33333333x2 + x4 = -12 + 38.02777776 Combine like terms: -12 + 38.02777776 = 26.02777776 38.02777776 + -12.33333333x2 + x4 = 26.02777776 Factor a perfect square on the left side: (x2 + -6.166666665)(x2 + -6.166666665) = 26.02777776 Calculate the square root of the right side: 5.10174262 Break this problem into two subproblems by setting (x2 + -6.166666665) equal to 5.10174262 and -5.10174262.Subproblem 1
x2 + -6.166666665 = 5.10174262 Simplifying x2 + -6.166666665 = 5.10174262 Reorder the terms: -6.166666665 + x2 = 5.10174262 Solving -6.166666665 + x2 = 5.10174262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.166666665' to each side of the equation. -6.166666665 + 6.166666665 + x2 = 5.10174262 + 6.166666665 Combine like terms: -6.166666665 + 6.166666665 = 0.000000000 0.000000000 + x2 = 5.10174262 + 6.166666665 x2 = 5.10174262 + 6.166666665 Combine like terms: 5.10174262 + 6.166666665 = 11.268409285 x2 = 11.268409285 Simplifying x2 = 11.268409285 Take the square root of each side: x = {-3.356845139, 3.356845139}Subproblem 2
x2 + -6.166666665 = -5.10174262 Simplifying x2 + -6.166666665 = -5.10174262 Reorder the terms: -6.166666665 + x2 = -5.10174262 Solving -6.166666665 + x2 = -5.10174262 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.166666665' to each side of the equation. -6.166666665 + 6.166666665 + x2 = -5.10174262 + 6.166666665 Combine like terms: -6.166666665 + 6.166666665 = 0.000000000 0.000000000 + x2 = -5.10174262 + 6.166666665 x2 = -5.10174262 + 6.166666665 Combine like terms: -5.10174262 + 6.166666665 = 1.064924045 x2 = 1.064924045 Simplifying x2 = 1.064924045 Take the square root of each side: x = {-1.031951571, 1.031951571}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.356845139, 3.356845139, -1.031951571, 1.031951571}
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