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Simplifying 0.012x2 + -0.543x + 35.727 = 40 Reorder the terms: 35.727 + -0.543x + 0.012x2 = 40 Solving 35.727 + -0.543x + 0.012x2 = 40 Solving for variable 'x'. Reorder the terms: 35.727 + -40 + -0.543x + 0.012x2 = 40 + -40 Combine like terms: 35.727 + -40 = -4.273 -4.273 + -0.543x + 0.012x2 = 40 + -40 Combine like terms: 40 + -40 = 0 -4.273 + -0.543x + 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'. -356.0833333 + -45.25x + x2 = 0 Move the constant term to the right: Add '356.0833333' to each side of the equation. -356.0833333 + -45.25x + 356.0833333 + x2 = 0 + 356.0833333 Reorder the terms: -356.0833333 + 356.0833333 + -45.25x + x2 = 0 + 356.0833333 Combine like terms: -356.0833333 + 356.0833333 = 0.0000000 0.0000000 + -45.25x + x2 = 0 + 356.0833333 -45.25x + x2 = 0 + 356.0833333 Combine like terms: 0 + 356.0833333 = 356.0833333 -45.25x + x2 = 356.0833333 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 = 356.0833333 + 511.890625 Reorder the terms: 511.890625 + -45.25x + x2 = 356.0833333 + 511.890625 Combine like terms: 356.0833333 + 511.890625 = 867.9739583 511.890625 + -45.25x + x2 = 867.9739583 Factor a perfect square on the left side: (x + -22.625)(x + -22.625) = 867.9739583 Calculate the square root of the right side: 29.461397766 Break this problem into two subproblems by setting (x + -22.625) equal to 29.461397766 and -29.461397766.Subproblem 1
x + -22.625 = 29.461397766 Simplifying x + -22.625 = 29.461397766 Reorder the terms: -22.625 + x = 29.461397766 Solving -22.625 + x = 29.461397766 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 = 29.461397766 + 22.625 Combine like terms: -22.625 + 22.625 = 0.000 0.000 + x = 29.461397766 + 22.625 x = 29.461397766 + 22.625 Combine like terms: 29.461397766 + 22.625 = 52.086397766 x = 52.086397766 Simplifying x = 52.086397766Subproblem 2
x + -22.625 = -29.461397766 Simplifying x + -22.625 = -29.461397766 Reorder the terms: -22.625 + x = -29.461397766 Solving -22.625 + x = -29.461397766 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 = -29.461397766 + 22.625 Combine like terms: -22.625 + 22.625 = 0.000 0.000 + x = -29.461397766 + 22.625 x = -29.461397766 + 22.625 Combine like terms: -29.461397766 + 22.625 = -6.836397766 x = -6.836397766 Simplifying x = -6.836397766Solution
The solution to the problem is based on the solutions from the subproblems. x = {52.086397766, -6.836397766}
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