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Simplifying 0.5 = 3.13x + 4.905(x2) Solving 0.5 = 3.13x + 4.905x2 Solving for variable 'x'. Reorder the terms: 0.5 + -3.13x + -4.905x2 = 3.13x + -3.13x + 4.905x2 + -4.905x2 Combine like terms: 3.13x + -3.13x = 0.00 0.5 + -3.13x + -4.905x2 = 0.00 + 4.905x2 + -4.905x2 0.5 + -3.13x + -4.905x2 = 4.905x2 + -4.905x2 Combine like terms: 4.905x2 + -4.905x2 = 0.000 0.5 + -3.13x + -4.905x2 = 0.000 Begin completing the square. Divide all terms by -4.905 the coefficient of the squared term: Divide each side by '-4.905'. -0.1019367992 + 0.6381243629x + x2 = 0 Move the constant term to the right: Add '0.1019367992' to each side of the equation. -0.1019367992 + 0.6381243629x + 0.1019367992 + x2 = 0 + 0.1019367992 Reorder the terms: -0.1019367992 + 0.1019367992 + 0.6381243629x + x2 = 0 + 0.1019367992 Combine like terms: -0.1019367992 + 0.1019367992 = 0.0000000000 0.0000000000 + 0.6381243629x + x2 = 0 + 0.1019367992 0.6381243629x + x2 = 0 + 0.1019367992 Combine like terms: 0 + 0.1019367992 = 0.1019367992 0.6381243629x + x2 = 0.1019367992 The x term is 0.6381243629x. Take half its coefficient (0.3190621815). Square it (0.1018006757) and add it to both sides. Add '0.1018006757' to each side of the equation. 0.6381243629x + 0.1018006757 + x2 = 0.1019367992 + 0.1018006757 Reorder the terms: 0.1018006757 + 0.6381243629x + x2 = 0.1019367992 + 0.1018006757 Combine like terms: 0.1019367992 + 0.1018006757 = 0.2037374749 0.1018006757 + 0.6381243629x + x2 = 0.2037374749 Factor a perfect square on the left side: (x + 0.3190621815)(x + 0.3190621815) = 0.2037374749 Calculate the square root of the right side: 0.451372878 Break this problem into two subproblems by setting (x + 0.3190621815) equal to 0.451372878 and -0.451372878.Subproblem 1
x + 0.3190621815 = 0.451372878 Simplifying x + 0.3190621815 = 0.451372878 Reorder the terms: 0.3190621815 + x = 0.451372878 Solving 0.3190621815 + x = 0.451372878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3190621815' to each side of the equation. 0.3190621815 + -0.3190621815 + x = 0.451372878 + -0.3190621815 Combine like terms: 0.3190621815 + -0.3190621815 = 0.0000000000 0.0000000000 + x = 0.451372878 + -0.3190621815 x = 0.451372878 + -0.3190621815 Combine like terms: 0.451372878 + -0.3190621815 = 0.1323106965 x = 0.1323106965 Simplifying x = 0.1323106965Subproblem 2
x + 0.3190621815 = -0.451372878 Simplifying x + 0.3190621815 = -0.451372878 Reorder the terms: 0.3190621815 + x = -0.451372878 Solving 0.3190621815 + x = -0.451372878 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3190621815' to each side of the equation. 0.3190621815 + -0.3190621815 + x = -0.451372878 + -0.3190621815 Combine like terms: 0.3190621815 + -0.3190621815 = 0.0000000000 0.0000000000 + x = -0.451372878 + -0.3190621815 x = -0.451372878 + -0.3190621815 Combine like terms: -0.451372878 + -0.3190621815 = -0.7704350595 x = -0.7704350595 Simplifying x = -0.7704350595Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.1323106965, -0.7704350595}
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