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Simplifying 35x4 + -26x2 + 1 = 0 Reorder the terms: 1 + -26x2 + 35x4 = 0 Solving 1 + -26x2 + 35x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. 0.02857142857 + -0.7428571429x2 + x4 = 0 Move the constant term to the right: Add '-0.02857142857' to each side of the equation. 0.02857142857 + -0.7428571429x2 + -0.02857142857 + x4 = 0 + -0.02857142857 Reorder the terms: 0.02857142857 + -0.02857142857 + -0.7428571429x2 + x4 = 0 + -0.02857142857 Combine like terms: 0.02857142857 + -0.02857142857 = 0.00000000000 0.00000000000 + -0.7428571429x2 + x4 = 0 + -0.02857142857 -0.7428571429x2 + x4 = 0 + -0.02857142857 Combine like terms: 0 + -0.02857142857 = -0.02857142857 -0.7428571429x2 + x4 = -0.02857142857 The x term is -0.7428571429x2. Take half its coefficient (-0.3714285715). Square it (0.1379591837) and add it to both sides. Add '0.1379591837' to each side of the equation. -0.7428571429x2 + 0.1379591837 + x4 = -0.02857142857 + 0.1379591837 Reorder the terms: 0.1379591837 + -0.7428571429x2 + x4 = -0.02857142857 + 0.1379591837 Combine like terms: -0.02857142857 + 0.1379591837 = 0.10938775513 0.1379591837 + -0.7428571429x2 + x4 = 0.10938775513 Factor a perfect square on the left side: (x2 + -0.3714285715)(x2 + -0.3714285715) = 0.10938775513 Calculate the square root of the right side: 0.330738197 Break this problem into two subproblems by setting (x2 + -0.3714285715) equal to 0.330738197 and -0.330738197.Subproblem 1
x2 + -0.3714285715 = 0.330738197 Simplifying x2 + -0.3714285715 = 0.330738197 Reorder the terms: -0.3714285715 + x2 = 0.330738197 Solving -0.3714285715 + x2 = 0.330738197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3714285715' to each side of the equation. -0.3714285715 + 0.3714285715 + x2 = 0.330738197 + 0.3714285715 Combine like terms: -0.3714285715 + 0.3714285715 = 0.0000000000 0.0000000000 + x2 = 0.330738197 + 0.3714285715 x2 = 0.330738197 + 0.3714285715 Combine like terms: 0.330738197 + 0.3714285715 = 0.7021667685 x2 = 0.7021667685 Simplifying x2 = 0.7021667685 Take the square root of each side: x = {-0.837953918, 0.837953918}Subproblem 2
x2 + -0.3714285715 = -0.330738197 Simplifying x2 + -0.3714285715 = -0.330738197 Reorder the terms: -0.3714285715 + x2 = -0.330738197 Solving -0.3714285715 + x2 = -0.330738197 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3714285715' to each side of the equation. -0.3714285715 + 0.3714285715 + x2 = -0.330738197 + 0.3714285715 Combine like terms: -0.3714285715 + 0.3714285715 = 0.0000000000 0.0000000000 + x2 = -0.330738197 + 0.3714285715 x2 = -0.330738197 + 0.3714285715 Combine like terms: -0.330738197 + 0.3714285715 = 0.0406903745 x2 = 0.0406903745 Simplifying x2 = 0.0406903745 Take the square root of each side: x = {-0.201718553, 0.201718553}Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.837953918, 0.837953918, -0.201718553, 0.201718553}
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