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Simplifying 0.179x2 + 0.029x + -0.463 = 0 Reorder the terms: -0.463 + 0.029x + 0.179x2 = 0 Solving -0.463 + 0.029x + 0.179x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.179 the coefficient of the squared term: Divide each side by '0.179'. -2.586592179 + 0.1620111732x + x2 = 0 Move the constant term to the right: Add '2.586592179' to each side of the equation. -2.586592179 + 0.1620111732x + 2.586592179 + x2 = 0 + 2.586592179 Reorder the terms: -2.586592179 + 2.586592179 + 0.1620111732x + x2 = 0 + 2.586592179 Combine like terms: -2.586592179 + 2.586592179 = 0.000000000 0.000000000 + 0.1620111732x + x2 = 0 + 2.586592179 0.1620111732x + x2 = 0 + 2.586592179 Combine like terms: 0 + 2.586592179 = 2.586592179 0.1620111732x + x2 = 2.586592179 The x term is 0.1620111732x. Take half its coefficient (0.0810055866). Square it (0.006561905060) and add it to both sides. Add '0.006561905060' to each side of the equation. 0.1620111732x + 0.006561905060 + x2 = 2.586592179 + 0.006561905060 Reorder the terms: 0.006561905060 + 0.1620111732x + x2 = 2.586592179 + 0.006561905060 Combine like terms: 2.586592179 + 0.006561905060 = 2.59315408406 0.006561905060 + 0.1620111732x + x2 = 2.59315408406 Factor a perfect square on the left side: (x + 0.0810055866)(x + 0.0810055866) = 2.59315408406 Calculate the square root of the right side: 1.610327322 Break this problem into two subproblems by setting (x + 0.0810055866) equal to 1.610327322 and -1.610327322.Subproblem 1
x + 0.0810055866 = 1.610327322 Simplifying x + 0.0810055866 = 1.610327322 Reorder the terms: 0.0810055866 + x = 1.610327322 Solving 0.0810055866 + x = 1.610327322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0810055866' to each side of the equation. 0.0810055866 + -0.0810055866 + x = 1.610327322 + -0.0810055866 Combine like terms: 0.0810055866 + -0.0810055866 = 0.0000000000 0.0000000000 + x = 1.610327322 + -0.0810055866 x = 1.610327322 + -0.0810055866 Combine like terms: 1.610327322 + -0.0810055866 = 1.5293217354 x = 1.5293217354 Simplifying x = 1.5293217354Subproblem 2
x + 0.0810055866 = -1.610327322 Simplifying x + 0.0810055866 = -1.610327322 Reorder the terms: 0.0810055866 + x = -1.610327322 Solving 0.0810055866 + x = -1.610327322 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0810055866' to each side of the equation. 0.0810055866 + -0.0810055866 + x = -1.610327322 + -0.0810055866 Combine like terms: 0.0810055866 + -0.0810055866 = 0.0000000000 0.0000000000 + x = -1.610327322 + -0.0810055866 x = -1.610327322 + -0.0810055866 Combine like terms: -1.610327322 + -0.0810055866 = -1.6913329086 x = -1.6913329086 Simplifying x = -1.6913329086Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5293217354, -1.6913329086}
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