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Simplifying 4x4 + -37x2 + 3x4 + -37x2 + 36 + 9 = 0 Reorder the terms: 36 + 9 + -37x2 + -37x2 + 4x4 + 3x4 = 0 Combine like terms: 36 + 9 = 45 45 + -37x2 + -37x2 + 4x4 + 3x4 = 0 Combine like terms: -37x2 + -37x2 = -74x2 45 + -74x2 + 4x4 + 3x4 = 0 Combine like terms: 4x4 + 3x4 = 7x4 45 + -74x2 + 7x4 = 0 Solving 45 + -74x2 + 7x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 6.428571429 + -10.57142857x2 + x4 = 0 Move the constant term to the right: Add '-6.428571429' to each side of the equation. 6.428571429 + -10.57142857x2 + -6.428571429 + x4 = 0 + -6.428571429 Reorder the terms: 6.428571429 + -6.428571429 + -10.57142857x2 + x4 = 0 + -6.428571429 Combine like terms: 6.428571429 + -6.428571429 = 0.000000000 0.000000000 + -10.57142857x2 + x4 = 0 + -6.428571429 -10.57142857x2 + x4 = 0 + -6.428571429 Combine like terms: 0 + -6.428571429 = -6.428571429 -10.57142857x2 + x4 = -6.428571429 The x term is -10.57142857x2. Take half its coefficient (-5.285714285). Square it (27.93877550) and add it to both sides. Add '27.93877550' to each side of the equation. -10.57142857x2 + 27.93877550 + x4 = -6.428571429 + 27.93877550 Reorder the terms: 27.93877550 + -10.57142857x2 + x4 = -6.428571429 + 27.93877550 Combine like terms: -6.428571429 + 27.93877550 = 21.510204071 27.93877550 + -10.57142857x2 + x4 = 21.510204071 Factor a perfect square on the left side: (x2 + -5.285714285)(x2 + -5.285714285) = 21.510204071 Calculate the square root of the right side: 4.63790945 Break this problem into two subproblems by setting (x2 + -5.285714285) equal to 4.63790945 and -4.63790945.Subproblem 1
x2 + -5.285714285 = 4.63790945 Simplifying x2 + -5.285714285 = 4.63790945 Reorder the terms: -5.285714285 + x2 = 4.63790945 Solving -5.285714285 + x2 = 4.63790945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.285714285' to each side of the equation. -5.285714285 + 5.285714285 + x2 = 4.63790945 + 5.285714285 Combine like terms: -5.285714285 + 5.285714285 = 0.000000000 0.000000000 + x2 = 4.63790945 + 5.285714285 x2 = 4.63790945 + 5.285714285 Combine like terms: 4.63790945 + 5.285714285 = 9.923623735 x2 = 9.923623735 Simplifying x2 = 9.923623735 Take the square root of each side: x = {-3.150178366, 3.150178366}Subproblem 2
x2 + -5.285714285 = -4.63790945 Simplifying x2 + -5.285714285 = -4.63790945 Reorder the terms: -5.285714285 + x2 = -4.63790945 Solving -5.285714285 + x2 = -4.63790945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.285714285' to each side of the equation. -5.285714285 + 5.285714285 + x2 = -4.63790945 + 5.285714285 Combine like terms: -5.285714285 + 5.285714285 = 0.000000000 0.000000000 + x2 = -4.63790945 + 5.285714285 x2 = -4.63790945 + 5.285714285 Combine like terms: -4.63790945 + 5.285714285 = 0.647804835 x2 = 0.647804835 Simplifying x2 = 0.647804835 Take the square root of each side: x = {-0.80486324, 0.80486324}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.150178366, 3.150178366, -0.80486324, 0.80486324}
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