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Simplifying 0.012x2 + -0.583x + 35.727 = 55 Reorder the terms: 35.727 + -0.583x + 0.012x2 = 55 Solving 35.727 + -0.583x + 0.012x2 = 55 Solving for variable 'x'. Reorder the terms: 35.727 + -55 + -0.583x + 0.012x2 = 55 + -55 Combine like terms: 35.727 + -55 = -19.273 -19.273 + -0.583x + 0.012x2 = 55 + -55 Combine like terms: 55 + -55 = 0 -19.273 + -0.583x + 0.012x2 = 0 Begin completing the square. Divide all terms by 0.012 the coefficient of the squared term: Divide each side by '0.012'. -1606.083333 + -48.58333333x + x2 = 0 Move the constant term to the right: Add '1606.083333' to each side of the equation. -1606.083333 + -48.58333333x + 1606.083333 + x2 = 0 + 1606.083333 Reorder the terms: -1606.083333 + 1606.083333 + -48.58333333x + x2 = 0 + 1606.083333 Combine like terms: -1606.083333 + 1606.083333 = 0.000000 0.000000 + -48.58333333x + x2 = 0 + 1606.083333 -48.58333333x + x2 = 0 + 1606.083333 Combine like terms: 0 + 1606.083333 = 1606.083333 -48.58333333x + x2 = 1606.083333 The x term is -48.58333333x. Take half its coefficient (-24.29166667). Square it (590.0850696) and add it to both sides. Add '590.0850696' to each side of the equation. -48.58333333x + 590.0850696 + x2 = 1606.083333 + 590.0850696 Reorder the terms: 590.0850696 + -48.58333333x + x2 = 1606.083333 + 590.0850696 Combine like terms: 1606.083333 + 590.0850696 = 2196.1684026 590.0850696 + -48.58333333x + x2 = 2196.1684026 Factor a perfect square on the left side: (x + -24.29166667)(x + -24.29166667) = 2196.1684026 Calculate the square root of the right side: 46.863294833 Break this problem into two subproblems by setting (x + -24.29166667) equal to 46.863294833 and -46.863294833.Subproblem 1
x + -24.29166667 = 46.863294833 Simplifying x + -24.29166667 = 46.863294833 Reorder the terms: -24.29166667 + x = 46.863294833 Solving -24.29166667 + x = 46.863294833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.29166667' to each side of the equation. -24.29166667 + 24.29166667 + x = 46.863294833 + 24.29166667 Combine like terms: -24.29166667 + 24.29166667 = 0.00000000 0.00000000 + x = 46.863294833 + 24.29166667 x = 46.863294833 + 24.29166667 Combine like terms: 46.863294833 + 24.29166667 = 71.154961503 x = 71.154961503 Simplifying x = 71.154961503Subproblem 2
x + -24.29166667 = -46.863294833 Simplifying x + -24.29166667 = -46.863294833 Reorder the terms: -24.29166667 + x = -46.863294833 Solving -24.29166667 + x = -46.863294833 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '24.29166667' to each side of the equation. -24.29166667 + 24.29166667 + x = -46.863294833 + 24.29166667 Combine like terms: -24.29166667 + 24.29166667 = 0.00000000 0.00000000 + x = -46.863294833 + 24.29166667 x = -46.863294833 + 24.29166667 Combine like terms: -46.863294833 + 24.29166667 = -22.571628163 x = -22.571628163 Simplifying x = -22.571628163Solution
The solution to the problem is based on the solutions from the subproblems. x = {71.154961503, -22.571628163}
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