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Simplifying 325x + -170.05625(1 + x2) = -65 325x + (1 * -170.05625 + x2 * -170.05625) = -65 325x + (-170.05625 + -170.05625x2) = -65 Reorder the terms: -170.05625 + 325x + -170.05625x2 = -65 Solving -170.05625 + 325x + -170.05625x2 = -65 Solving for variable 'x'. Reorder the terms: -170.05625 + 65 + 325x + -170.05625x2 = -65 + 65 Combine like terms: -170.05625 + 65 = -105.05625 -105.05625 + 325x + -170.05625x2 = -65 + 65 Combine like terms: -65 + 65 = 0 -105.05625 + 325x + -170.05625x2 = 0 Begin completing the square. Divide all terms by -170.05625 the coefficient of the squared term: Divide each side by '-170.05625'. 0.6177735308 + -1.911132346x + x2 = 0 Move the constant term to the right: Add '-0.6177735308' to each side of the equation. 0.6177735308 + -1.911132346x + -0.6177735308 + x2 = 0 + -0.6177735308 Reorder the terms: 0.6177735308 + -0.6177735308 + -1.911132346x + x2 = 0 + -0.6177735308 Combine like terms: 0.6177735308 + -0.6177735308 = 0.0000000000 0.0000000000 + -1.911132346x + x2 = 0 + -0.6177735308 -1.911132346x + x2 = 0 + -0.6177735308 Combine like terms: 0 + -0.6177735308 = -0.6177735308 -1.911132346x + x2 = -0.6177735308 The x term is -1.911132346x. Take half its coefficient (-0.955566173). Square it (0.9131067110) and add it to both sides. Add '0.9131067110' to each side of the equation. -1.911132346x + 0.9131067110 + x2 = -0.6177735308 + 0.9131067110 Reorder the terms: 0.9131067110 + -1.911132346x + x2 = -0.6177735308 + 0.9131067110 Combine like terms: -0.6177735308 + 0.9131067110 = 0.2953331802 0.9131067110 + -1.911132346x + x2 = 0.2953331802 Factor a perfect square on the left side: (x + -0.955566173)(x + -0.955566173) = 0.2953331802 Calculate the square root of the right side: 0.543445655 Break this problem into two subproblems by setting (x + -0.955566173) equal to 0.543445655 and -0.543445655.Subproblem 1
x + -0.955566173 = 0.543445655 Simplifying x + -0.955566173 = 0.543445655 Reorder the terms: -0.955566173 + x = 0.543445655 Solving -0.955566173 + x = 0.543445655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.955566173' to each side of the equation. -0.955566173 + 0.955566173 + x = 0.543445655 + 0.955566173 Combine like terms: -0.955566173 + 0.955566173 = 0.000000000 0.000000000 + x = 0.543445655 + 0.955566173 x = 0.543445655 + 0.955566173 Combine like terms: 0.543445655 + 0.955566173 = 1.499011828 x = 1.499011828 Simplifying x = 1.499011828Subproblem 2
x + -0.955566173 = -0.543445655 Simplifying x + -0.955566173 = -0.543445655 Reorder the terms: -0.955566173 + x = -0.543445655 Solving -0.955566173 + x = -0.543445655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.955566173' to each side of the equation. -0.955566173 + 0.955566173 + x = -0.543445655 + 0.955566173 Combine like terms: -0.955566173 + 0.955566173 = 0.000000000 0.000000000 + x = -0.543445655 + 0.955566173 x = -0.543445655 + 0.955566173 Combine like terms: -0.543445655 + 0.955566173 = 0.412120518 x = 0.412120518 Simplifying x = 0.412120518Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.499011828, 0.412120518}
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