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Simplifying 0.012x2 + -0.583x + 35.7222 = 50 Reorder the terms: 35.7222 + -0.583x + 0.012x2 = 50 Solving 35.7222 + -0.583x + 0.012x2 = 50 Solving for variable 'x'. Reorder the terms: 35.7222 + -50 + -0.583x + 0.012x2 = 50 + -50 Combine like terms: 35.7222 + -50 = -14.2778 -14.2778 + -0.583x + 0.012x2 = 50 + -50 Combine like terms: 50 + -50 = 0 -14.2778 + -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'. -1189.816667 + -48.58333333x + x2 = 0 Move the constant term to the right: Add '1189.816667' to each side of the equation. -1189.816667 + -48.58333333x + 1189.816667 + x2 = 0 + 1189.816667 Reorder the terms: -1189.816667 + 1189.816667 + -48.58333333x + x2 = 0 + 1189.816667 Combine like terms: -1189.816667 + 1189.816667 = 0.000000 0.000000 + -48.58333333x + x2 = 0 + 1189.816667 -48.58333333x + x2 = 0 + 1189.816667 Combine like terms: 0 + 1189.816667 = 1189.816667 -48.58333333x + x2 = 1189.816667 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 = 1189.816667 + 590.0850696 Reorder the terms: 590.0850696 + -48.58333333x + x2 = 1189.816667 + 590.0850696 Combine like terms: 1189.816667 + 590.0850696 = 1779.9017366 590.0850696 + -48.58333333x + x2 = 1779.9017366 Factor a perfect square on the left side: (x + -24.29166667)(x + -24.29166667) = 1779.9017366 Calculate the square root of the right side: 42.18888167 Break this problem into two subproblems by setting (x + -24.29166667) equal to 42.18888167 and -42.18888167.Subproblem 1
x + -24.29166667 = 42.18888167 Simplifying x + -24.29166667 = 42.18888167 Reorder the terms: -24.29166667 + x = 42.18888167 Solving -24.29166667 + x = 42.18888167 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 = 42.18888167 + 24.29166667 Combine like terms: -24.29166667 + 24.29166667 = 0.00000000 0.00000000 + x = 42.18888167 + 24.29166667 x = 42.18888167 + 24.29166667 Combine like terms: 42.18888167 + 24.29166667 = 66.48054834 x = 66.48054834 Simplifying x = 66.48054834Subproblem 2
x + -24.29166667 = -42.18888167 Simplifying x + -24.29166667 = -42.18888167 Reorder the terms: -24.29166667 + x = -42.18888167 Solving -24.29166667 + x = -42.18888167 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 = -42.18888167 + 24.29166667 Combine like terms: -24.29166667 + 24.29166667 = 0.00000000 0.00000000 + x = -42.18888167 + 24.29166667 x = -42.18888167 + 24.29166667 Combine like terms: -42.18888167 + 24.29166667 = -17.897215 x = -17.897215 Simplifying x = -17.897215Solution
The solution to the problem is based on the solutions from the subproblems. x = {66.48054834, -17.897215}
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