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Simplifying 12x2 + -583x + 35727 = 40000 Reorder the terms: 35727 + -583x + 12x2 = 40000 Solving 35727 + -583x + 12x2 = 40000 Solving for variable 'x'. Reorder the terms: 35727 + -40000 + -583x + 12x2 = 40000 + -40000 Combine like terms: 35727 + -40000 = -4273 -4273 + -583x + 12x2 = 40000 + -40000 Combine like terms: 40000 + -40000 = 0 -4273 + -583x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -356.0833333 + -48.58333333x + x2 = 0 Move the constant term to the right: Add '356.0833333' to each side of the equation. -356.0833333 + -48.58333333x + 356.0833333 + x2 = 0 + 356.0833333 Reorder the terms: -356.0833333 + 356.0833333 + -48.58333333x + x2 = 0 + 356.0833333 Combine like terms: -356.0833333 + 356.0833333 = 0.0000000 0.0000000 + -48.58333333x + x2 = 0 + 356.0833333 -48.58333333x + x2 = 0 + 356.0833333 Combine like terms: 0 + 356.0833333 = 356.0833333 -48.58333333x + x2 = 356.0833333 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 = 356.0833333 + 590.0850696 Reorder the terms: 590.0850696 + -48.58333333x + x2 = 356.0833333 + 590.0850696 Combine like terms: 356.0833333 + 590.0850696 = 946.1684029 590.0850696 + -48.58333333x + x2 = 946.1684029 Factor a perfect square on the left side: (x + -24.29166667)(x + -24.29166667) = 946.1684029 Calculate the square root of the right side: 30.759850502 Break this problem into two subproblems by setting (x + -24.29166667) equal to 30.759850502 and -30.759850502.Subproblem 1
x + -24.29166667 = 30.759850502 Simplifying x + -24.29166667 = 30.759850502 Reorder the terms: -24.29166667 + x = 30.759850502 Solving -24.29166667 + x = 30.759850502 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 = 30.759850502 + 24.29166667 Combine like terms: -24.29166667 + 24.29166667 = 0.00000000 0.00000000 + x = 30.759850502 + 24.29166667 x = 30.759850502 + 24.29166667 Combine like terms: 30.759850502 + 24.29166667 = 55.051517172 x = 55.051517172 Simplifying x = 55.051517172Subproblem 2
x + -24.29166667 = -30.759850502 Simplifying x + -24.29166667 = -30.759850502 Reorder the terms: -24.29166667 + x = -30.759850502 Solving -24.29166667 + x = -30.759850502 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 = -30.759850502 + 24.29166667 Combine like terms: -24.29166667 + 24.29166667 = 0.00000000 0.00000000 + x = -30.759850502 + 24.29166667 x = -30.759850502 + 24.29166667 Combine like terms: -30.759850502 + 24.29166667 = -6.468183832 x = -6.468183832 Simplifying x = -6.468183832Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.051517172, -6.468183832}
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