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Simplifying 40 = 0.012x2 + -0.543x + 35.722 Reorder the terms: 40 = 35.722 + -0.543x + 0.012x2 Solving 40 = 35.722 + -0.543x + 0.012x2 Solving for variable 'x'. Combine like terms: 40 + -35.722 = 4.278 4.278 + 0.543x + -0.012x2 = 35.722 + -0.543x + 0.012x2 + -35.722 + 0.543x + -0.012x2 Reorder the terms: 4.278 + 0.543x + -0.012x2 = 35.722 + -35.722 + -0.543x + 0.543x + 0.012x2 + -0.012x2 Combine like terms: 35.722 + -35.722 = 0.000 4.278 + 0.543x + -0.012x2 = 0.000 + -0.543x + 0.543x + 0.012x2 + -0.012x2 4.278 + 0.543x + -0.012x2 = -0.543x + 0.543x + 0.012x2 + -0.012x2 Combine like terms: -0.543x + 0.543x = 0.000 4.278 + 0.543x + -0.012x2 = 0.000 + 0.012x2 + -0.012x2 4.278 + 0.543x + -0.012x2 = 0.012x2 + -0.012x2 Combine like terms: 0.012x2 + -0.012x2 = 0.000 4.278 + 0.543x + -0.012x2 = 0.000 Begin completing the square. Divide all terms by -0.012 the coefficient of the squared term: Divide each side by '-0.012'. -356.5 + -45.25x + x2 = 0 Move the constant term to the right: Add '356.5' to each side of the equation. -356.5 + -45.25x + 356.5 + x2 = 0 + 356.5 Reorder the terms: -356.5 + 356.5 + -45.25x + x2 = 0 + 356.5 Combine like terms: -356.5 + 356.5 = 0.0 0.0 + -45.25x + x2 = 0 + 356.5 -45.25x + x2 = 0 + 356.5 Combine like terms: 0 + 356.5 = 356.5 -45.25x + x2 = 356.5 The x term is -45.25x. Take half its coefficient (-22.625). Square it (511.890625) and add it to both sides. Add '511.890625' to each side of the equation. -45.25x + 511.890625 + x2 = 356.5 + 511.890625 Reorder the terms: 511.890625 + -45.25x + x2 = 356.5 + 511.890625 Combine like terms: 356.5 + 511.890625 = 868.390625 511.890625 + -45.25x + x2 = 868.390625 Factor a perfect square on the left side: (x + -22.625)(x + -22.625) = 868.390625 Calculate the square root of the right side: 29.468468318 Break this problem into two subproblems by setting (x + -22.625) equal to 29.468468318 and -29.468468318.Subproblem 1
x + -22.625 = 29.468468318 Simplifying x + -22.625 = 29.468468318 Reorder the terms: -22.625 + x = 29.468468318 Solving -22.625 + x = 29.468468318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.625' to each side of the equation. -22.625 + 22.625 + x = 29.468468318 + 22.625 Combine like terms: -22.625 + 22.625 = 0.000 0.000 + x = 29.468468318 + 22.625 x = 29.468468318 + 22.625 Combine like terms: 29.468468318 + 22.625 = 52.093468318 x = 52.093468318 Simplifying x = 52.093468318Subproblem 2
x + -22.625 = -29.468468318 Simplifying x + -22.625 = -29.468468318 Reorder the terms: -22.625 + x = -29.468468318 Solving -22.625 + x = -29.468468318 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '22.625' to each side of the equation. -22.625 + 22.625 + x = -29.468468318 + 22.625 Combine like terms: -22.625 + 22.625 = 0.000 0.000 + x = -29.468468318 + 22.625 x = -29.468468318 + 22.625 Combine like terms: -29.468468318 + 22.625 = -6.843468318 x = -6.843468318 Simplifying x = -6.843468318Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.093468318, -6.843468318}
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