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Simplifying 0.0484x4 + -8.41x2 + -784 = 0 Reorder the terms: -784 + -8.41x2 + 0.0484x4 = 0 Solving -784 + -8.41x2 + 0.0484x4 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.0484 the coefficient of the squared term: Divide each side by '0.0484'. -16198.34711 + -173.7603306x2 + x4 = 0 Move the constant term to the right: Add '16198.34711' to each side of the equation. -16198.34711 + -173.7603306x2 + 16198.34711 + x4 = 0 + 16198.34711 Reorder the terms: -16198.34711 + 16198.34711 + -173.7603306x2 + x4 = 0 + 16198.34711 Combine like terms: -16198.34711 + 16198.34711 = 0.00000 0.00000 + -173.7603306x2 + x4 = 0 + 16198.34711 -173.7603306x2 + x4 = 0 + 16198.34711 Combine like terms: 0 + 16198.34711 = 16198.34711 -173.7603306x2 + x4 = 16198.34711 The x term is -173.7603306x2. Take half its coefficient (-86.8801653). Square it (7548.163123) and add it to both sides. Add '7548.163123' to each side of the equation. -173.7603306x2 + 7548.163123 + x4 = 16198.34711 + 7548.163123 Reorder the terms: 7548.163123 + -173.7603306x2 + x4 = 16198.34711 + 7548.163123 Combine like terms: 16198.34711 + 7548.163123 = 23746.510233 7548.163123 + -173.7603306x2 + x4 = 23746.510233 Factor a perfect square on the left side: (x2 + -86.8801653)(x2 + -86.8801653) = 23746.510233 Calculate the square root of the right side: 154.099027359 Break this problem into two subproblems by setting (x2 + -86.8801653) equal to 154.099027359 and -154.099027359.Subproblem 1
x2 + -86.8801653 = 154.099027359 Simplifying x2 + -86.8801653 = 154.099027359 Reorder the terms: -86.8801653 + x2 = 154.099027359 Solving -86.8801653 + x2 = 154.099027359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '86.8801653' to each side of the equation. -86.8801653 + 86.8801653 + x2 = 154.099027359 + 86.8801653 Combine like terms: -86.8801653 + 86.8801653 = 0.0000000 0.0000000 + x2 = 154.099027359 + 86.8801653 x2 = 154.099027359 + 86.8801653 Combine like terms: 154.099027359 + 86.8801653 = 240.979192659 x2 = 240.979192659 Simplifying x2 = 240.979192659 Take the square root of each side: x = {-15.523504522, 15.523504522}Subproblem 2
x2 + -86.8801653 = -154.099027359 Simplifying x2 + -86.8801653 = -154.099027359 Reorder the terms: -86.8801653 + x2 = -154.099027359 Solving -86.8801653 + x2 = -154.099027359 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '86.8801653' to each side of the equation. -86.8801653 + 86.8801653 + x2 = -154.099027359 + 86.8801653 Combine like terms: -86.8801653 + 86.8801653 = 0.0000000 0.0000000 + x2 = -154.099027359 + 86.8801653 x2 = -154.099027359 + 86.8801653 Combine like terms: -154.099027359 + 86.8801653 = -67.218862059 x2 = -67.218862059 Simplifying x2 = -67.218862059 Reorder the terms: 67.218862059 + x2 = -67.218862059 + 67.218862059 Combine like terms: -67.218862059 + 67.218862059 = 0.000000000 67.218862059 + x2 = 0.000000000 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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