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Simplifying 0.012x2 + -0.583x + 35.725 + -40 = 0 Reorder the terms: 35.725 + -40 + -0.583x + 0.012x2 = 0 Combine like terms: 35.725 + -40 = -4.275 -4.275 + -0.583x + 0.012x2 = 0 Solving -4.275 + -0.583x + 0.012x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.012 the coefficient of the squared term: Divide each side by '0.012'. -356.25 + -48.58333333x + x2 = 0 Move the constant term to the right: Add '356.25' to each side of the equation. -356.25 + -48.58333333x + 356.25 + x2 = 0 + 356.25 Reorder the terms: -356.25 + 356.25 + -48.58333333x + x2 = 0 + 356.25 Combine like terms: -356.25 + 356.25 = 0.00 0.00 + -48.58333333x + x2 = 0 + 356.25 -48.58333333x + x2 = 0 + 356.25 Combine like terms: 0 + 356.25 = 356.25 -48.58333333x + x2 = 356.25 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 = 356.25 + 590.0850696 Reorder the terms: 590.0850696 + -48.58333333x + x2 = 356.25 + 590.0850696 Combine like terms: 356.25 + 590.0850696 = 946.3350696 590.0850696 + -48.58333333x + x2 = 946.3350696 Factor a perfect square on the left side: (x + -24.29166667)(x + -24.29166667) = 946.3350696 Calculate the square root of the right side: 30.762559542 Break this problem into two subproblems by setting (x + -24.29166667) equal to 30.762559542 and -30.762559542.Subproblem 1
x + -24.29166667 = 30.762559542 Simplifying x + -24.29166667 = 30.762559542 Reorder the terms: -24.29166667 + x = 30.762559542 Solving -24.29166667 + x = 30.762559542 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 = 30.762559542 + 24.29166667 Combine like terms: -24.29166667 + 24.29166667 = 0.00000000 0.00000000 + x = 30.762559542 + 24.29166667 x = 30.762559542 + 24.29166667 Combine like terms: 30.762559542 + 24.29166667 = 55.054226212 x = 55.054226212 Simplifying x = 55.054226212Subproblem 2
x + -24.29166667 = -30.762559542 Simplifying x + -24.29166667 = -30.762559542 Reorder the terms: -24.29166667 + x = -30.762559542 Solving -24.29166667 + x = -30.762559542 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 = -30.762559542 + 24.29166667 Combine like terms: -24.29166667 + 24.29166667 = 0.00000000 0.00000000 + x = -30.762559542 + 24.29166667 x = -30.762559542 + 24.29166667 Combine like terms: -30.762559542 + 24.29166667 = -6.470892872 x = -6.470892872 Simplifying x = -6.470892872Solution
The solution to the problem is based on the solutions from the subproblems. x = {55.054226212, -6.470892872}
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