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Simplifying 17.89x4 + 25.6x2 + 9.13 = 0 Reorder the terms: 9.13 + 25.6x2 + 17.89x4 = 0 Solving 9.13 + 25.6x2 + 17.89x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17.89 the coefficient of the squared term: Divide each side by '17.89'. 0.5103409726 + 1.430967021x2 + x4 = 0 Move the constant term to the right: Add '-0.5103409726' to each side of the equation. 0.5103409726 + 1.430967021x2 + -0.5103409726 + x4 = 0 + -0.5103409726 Reorder the terms: 0.5103409726 + -0.5103409726 + 1.430967021x2 + x4 = 0 + -0.5103409726 Combine like terms: 0.5103409726 + -0.5103409726 = 0.0000000000 0.0000000000 + 1.430967021x2 + x4 = 0 + -0.5103409726 1.430967021x2 + x4 = 0 + -0.5103409726 Combine like terms: 0 + -0.5103409726 = -0.5103409726 1.430967021x2 + x4 = -0.5103409726 The x term is 1.430967021x2. Take half its coefficient (0.7154835105). Square it (0.5119166538) and add it to both sides. Add '0.5119166538' to each side of the equation. 1.430967021x2 + 0.5119166538 + x4 = -0.5103409726 + 0.5119166538 Reorder the terms: 0.5119166538 + 1.430967021x2 + x4 = -0.5103409726 + 0.5119166538 Combine like terms: -0.5103409726 + 0.5119166538 = 0.0015756812 0.5119166538 + 1.430967021x2 + x4 = 0.0015756812 Factor a perfect square on the left side: (x2 + 0.7154835105)(x2 + 0.7154835105) = 0.0015756812 Calculate the square root of the right side: 0.039694851 Break this problem into two subproblems by setting (x2 + 0.7154835105) equal to 0.039694851 and -0.039694851.Subproblem 1
x2 + 0.7154835105 = 0.039694851 Simplifying x2 + 0.7154835105 = 0.039694851 Reorder the terms: 0.7154835105 + x2 = 0.039694851 Solving 0.7154835105 + x2 = 0.039694851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7154835105' to each side of the equation. 0.7154835105 + -0.7154835105 + x2 = 0.039694851 + -0.7154835105 Combine like terms: 0.7154835105 + -0.7154835105 = 0.0000000000 0.0000000000 + x2 = 0.039694851 + -0.7154835105 x2 = 0.039694851 + -0.7154835105 Combine like terms: 0.039694851 + -0.7154835105 = -0.6757886595 x2 = -0.6757886595 Simplifying x2 = -0.6757886595 Reorder the terms: 0.6757886595 + x2 = -0.6757886595 + 0.6757886595 Combine like terms: -0.6757886595 + 0.6757886595 = 0.0000000000 0.6757886595 + x2 = 0.0000000000 The solution to this equation could not be determined.This subproblem is being ignored because a solution could not be determined.Subproblem 2
x2 + 0.7154835105 = -0.039694851 Simplifying x2 + 0.7154835105 = -0.039694851 Reorder the terms: 0.7154835105 + x2 = -0.039694851 Solving 0.7154835105 + x2 = -0.039694851 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.7154835105' to each side of the equation. 0.7154835105 + -0.7154835105 + x2 = -0.039694851 + -0.7154835105 Combine like terms: 0.7154835105 + -0.7154835105 = 0.0000000000 0.0000000000 + x2 = -0.039694851 + -0.7154835105 x2 = -0.039694851 + -0.7154835105 Combine like terms: -0.039694851 + -0.7154835105 = -0.7551783615 x2 = -0.7551783615 Simplifying x2 = -0.7551783615 Reorder the terms: 0.7551783615 + x2 = -0.7551783615 + 0.7551783615 Combine like terms: -0.7551783615 + 0.7551783615 = 0.0000000000 0.7551783615 + 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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