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Simplifying 7x4 + 5x2 + -10 = 0 Reorder the terms: -10 + 5x2 + 7x4 = 0 Solving -10 + 5x2 + 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'. -1.428571429 + 0.7142857143x2 + x4 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + 0.7142857143x2 + 1.428571429 + x4 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + 0.7142857143x2 + x4 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + 0.7142857143x2 + x4 = 0 + 1.428571429 0.7142857143x2 + x4 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 0.7142857143x2 + x4 = 1.428571429 The x term is 0.7142857143x2. Take half its coefficient (0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. 0.7142857143x2 + 0.1275510204 + x4 = 1.428571429 + 0.1275510204 Reorder the terms: 0.1275510204 + 0.7142857143x2 + x4 = 1.428571429 + 0.1275510204 Combine like terms: 1.428571429 + 0.1275510204 = 1.5561224494 0.1275510204 + 0.7142857143x2 + x4 = 1.5561224494 Factor a perfect square on the left side: (x2 + 0.3571428572)(x2 + 0.3571428572) = 1.5561224494 Calculate the square root of the right side: 1.247446371 Break this problem into two subproblems by setting (x2 + 0.3571428572) equal to 1.247446371 and -1.247446371.Subproblem 1
x2 + 0.3571428572 = 1.247446371 Simplifying x2 + 0.3571428572 = 1.247446371 Reorder the terms: 0.3571428572 + x2 = 1.247446371 Solving 0.3571428572 + x2 = 1.247446371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x2 = 1.247446371 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x2 = 1.247446371 + -0.3571428572 x2 = 1.247446371 + -0.3571428572 Combine like terms: 1.247446371 + -0.3571428572 = 0.8903035138 x2 = 0.8903035138 Simplifying x2 = 0.8903035138 Take the square root of each side: x = {-0.943558961, 0.943558961}Subproblem 2
x2 + 0.3571428572 = -1.247446371 Simplifying x2 + 0.3571428572 = -1.247446371 Reorder the terms: 0.3571428572 + x2 = -1.247446371 Solving 0.3571428572 + x2 = -1.247446371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + x2 = -1.247446371 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + x2 = -1.247446371 + -0.3571428572 x2 = -1.247446371 + -0.3571428572 Combine like terms: -1.247446371 + -0.3571428572 = -1.6045892282 x2 = -1.6045892282 Simplifying x2 = -1.6045892282 Reorder the terms: 1.6045892282 + x2 = -1.6045892282 + 1.6045892282 Combine like terms: -1.6045892282 + 1.6045892282 = 0.0000000000 1.6045892282 + x2 = 0.0000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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