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Simplifying 40 = 0.012x2 + -0.543x + 35.724 Reorder the terms: 40 = 35.724 + -0.543x + 0.012x2 Solving 40 = 35.724 + -0.543x + 0.012x2 Solving for variable 'x'. Combine like terms: 40 + -35.724 = 4.276 4.276 + 0.543x + -0.012x2 = 35.724 + -0.543x + 0.012x2 + -35.724 + 0.543x + -0.012x2 Reorder the terms: 4.276 + 0.543x + -0.012x2 = 35.724 + -35.724 + -0.543x + 0.543x + 0.012x2 + -0.012x2 Combine like terms: 35.724 + -35.724 = 0.000 4.276 + 0.543x + -0.012x2 = 0.000 + -0.543x + 0.543x + 0.012x2 + -0.012x2 4.276 + 0.543x + -0.012x2 = -0.543x + 0.543x + 0.012x2 + -0.012x2 Combine like terms: -0.543x + 0.543x = 0.000 4.276 + 0.543x + -0.012x2 = 0.000 + 0.012x2 + -0.012x2 4.276 + 0.543x + -0.012x2 = 0.012x2 + -0.012x2 Combine like terms: 0.012x2 + -0.012x2 = 0.000 4.276 + 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'. -356.3333333 + -45.25x + x2 = 0 Move the constant term to the right: Add '356.3333333' to each side of the equation. -356.3333333 + -45.25x + 356.3333333 + x2 = 0 + 356.3333333 Reorder the terms: -356.3333333 + 356.3333333 + -45.25x + x2 = 0 + 356.3333333 Combine like terms: -356.3333333 + 356.3333333 = 0.0000000 0.0000000 + -45.25x + x2 = 0 + 356.3333333 -45.25x + x2 = 0 + 356.3333333 Combine like terms: 0 + 356.3333333 = 356.3333333 -45.25x + x2 = 356.3333333 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 = 356.3333333 + 511.890625 Reorder the terms: 511.890625 + -45.25x + x2 = 356.3333333 + 511.890625 Combine like terms: 356.3333333 + 511.890625 = 868.2239583 511.890625 + -45.25x + x2 = 868.2239583 Factor a perfect square on the left side: (x + -22.625)(x + -22.625) = 868.2239583 Calculate the square root of the right side: 29.4656403 Break this problem into two subproblems by setting (x + -22.625) equal to 29.4656403 and -29.4656403.Subproblem 1
x + -22.625 = 29.4656403 Simplifying x + -22.625 = 29.4656403 Reorder the terms: -22.625 + x = 29.4656403 Solving -22.625 + x = 29.4656403 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 = 29.4656403 + 22.625 Combine like terms: -22.625 + 22.625 = 0.000 0.000 + x = 29.4656403 + 22.625 x = 29.4656403 + 22.625 Combine like terms: 29.4656403 + 22.625 = 52.0906403 x = 52.0906403 Simplifying x = 52.0906403Subproblem 2
x + -22.625 = -29.4656403 Simplifying x + -22.625 = -29.4656403 Reorder the terms: -22.625 + x = -29.4656403 Solving -22.625 + x = -29.4656403 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 = -29.4656403 + 22.625 Combine like terms: -22.625 + 22.625 = 0.000 0.000 + x = -29.4656403 + 22.625 x = -29.4656403 + 22.625 Combine like terms: -29.4656403 + 22.625 = -6.8406403 x = -6.8406403 Simplifying x = -6.8406403Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.0906403, -6.8406403}
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